A factory receives power at 480 Vrms @ 60 Hz. from the electric utility company. The factory’s electrical load can be simply represented by 2 loads. LOAD1 describes the manufacturing equipment on the assembly line. LOAD2 describes the power used in office rooms. From time to time, the assembly line shuts down thereby removing LOAD1 from the grid. SWITCH1 accounts for this effect in the equivalent circuit model shown above. Note that the 2 dependent sources represent a device called a “transformer” that steps the 480 Vrms down to 120 Vrms for use in the offices. (But don’t take my word for it; circuit analysis calculations will confirm this.) Given: Receiving End Voltage (with SWITCH1 closed): RV = 480 Vrms Wiring parameters: RW = 0.005 Ω, LW = 0.52052 mH Find: a) With SWITCH1 closed, find the value of C (in Farads) so that the total LOADt at the Receiving End has unity pf. Find the magnitude of the Sending End Voltage SV , and the magnitude of the “Office” load voltage, 2V. Note that RMS480VRV= for this case. b) With SWITCH1 open, using the value of C and SV found in part a), find the new values of the magnitudes of the Receiving End Voltage RV and Office Voltage 2V. Why will this be a problem for the office? How could you change the capacitor connection to avoid this problem? Hints: Note that no phase angles were given, and only magnitudes were asked for. You can choose one voltage or current to have 0 degree phase angle and then allow the calculations of any other voltages and currents be relative to that. In part b) RMS480VRV≠.

A factory receives power at 480 Vrms @ 60 Hz. from the electric utility company. The factory’s electrical load can be simply represented by 2 loads. LOAD1 describes the manufacturing equipment on the assembly line. LOAD2 describes the power used in office rooms. From time to time, the assembly line shuts down thereby removing LOAD1 from the grid. SWITCH1 accounts for this effect in the equivalent circuit model shown above. Note that the 2 dependent sources represent a device called a “transformer” that steps the 480 Vrms down to 120 Vrms for use in the offices. (But don’t take my word for it; circuit analysis calculations will confirm this.) Given: Receiving End Voltage (with SWITCH1 closed): RV = 480 Vrms Wiring parameters: RW = 0.005 Ω, LW = 0.52052 mH Find: a) With SWITCH1 closed, find the value of C (in Farads) so that the total LOADt at the Receiving End has unity pf. Find the magnitude of the Sending End Voltage SV , and the magnitude of the “Office” load voltage, 2V. Note that RMS480VRV= for this case. b) With SWITCH1 open, using the value of C and SV found in part a), find the new values of the magnitudes of the Receiving End Voltage RV and Office Voltage 2V. Why will this be a problem for the office? How could you change the capacitor connection to avoid this problem? Hints: Note that no phase angles were given, and only magnitudes were asked for. You can choose one voltage or current to have 0 degree phase angle and then allow the calculations of any other voltages and currents be relative to that. In part b) RMS480VRV≠.

A factory receives power at 480 Vrms @ 60 Hz. … Read More...
Lectorial 5: The Gravitron The Gravitron (shown in figure 1 [1]) is a carnival ride designed to simulate the experience of zero gravity. The ride consists of a 15 metre diameter circular chamber which spins around a centre shaft. The spinning motion applies a force to the occupants of the ride pinning them up against their seat. Figure 1: The Gravitron carnival ride. For this lectorial task we want to study the forces being applied to the ride’s occupants and determine the g-forces they would be experiencing. According to physics, the rules for uniform circular motion are: where: 1. If the ride has a maximum rotational speed of 24 revolutions per minute (rpm), determine the force being applied to the ride’s occupants. What gforces are the people experiencing (assume occupants are 65 kg adults)? [1] “Gravitron” used under Creative Commons licence (https://creativecommons.org/licenses/by-nc-sa/2.0/). Photo by: bobdole369 Newtons 2 r v F = ma = m angular speed in radians per second rotational speed in revolutions per second (or Hz) radius of the Gravitron tangential velocity of the Gravitron mass of occupant = = = = = w f r v m -1 v = wr ms w = 2pf rad/sec Typically the Gravitron ride takes approximately 20 seconds to reach its maximum rotational speed of 24 rpms and the whole ride lasts for around 80 seconds. This means the ride’s occupants are exposed to non-uniform circular motion meaning there is changing linear velocity at certain parts of the ride. For non-uniform circular motion the following formulae are useful: where: A GPS tracking device was attached to a person in the Gravitron and data was obtained about their x,y displacement vs. time over the 80 second duration of the ride. The data was saved in a .csv file called ‘gravitron.csv.’ This file contains three columns: time, x-displacement and y-displacement, e.g.: Time, sec x-displacement y-displacement 0.00 0.10 0.20 … 2. Download this .csv file from Blackboard. Find the g-forces being applied to the ride’s occupants for the whole 80 second duration of the ride. Again assume the occupants are 65 kg adults. Think about how you could effectively present these results. -2 2 ms r v -1 a = 2 2 ms     +     = dt dy dt dx v centripetal acceleration time in seconds displacement in y direction displacement in x direction = = = = a t y x

Lectorial 5: The Gravitron The Gravitron (shown in figure 1 [1]) is a carnival ride designed to simulate the experience of zero gravity. The ride consists of a 15 metre diameter circular chamber which spins around a centre shaft. The spinning motion applies a force to the occupants of the ride pinning them up against their seat. Figure 1: The Gravitron carnival ride. For this lectorial task we want to study the forces being applied to the ride’s occupants and determine the g-forces they would be experiencing. According to physics, the rules for uniform circular motion are: where: 1. If the ride has a maximum rotational speed of 24 revolutions per minute (rpm), determine the force being applied to the ride’s occupants. What gforces are the people experiencing (assume occupants are 65 kg adults)? [1] “Gravitron” used under Creative Commons licence (https://creativecommons.org/licenses/by-nc-sa/2.0/). Photo by: bobdole369 Newtons 2 r v F = ma = m angular speed in radians per second rotational speed in revolutions per second (or Hz) radius of the Gravitron tangential velocity of the Gravitron mass of occupant = = = = = w f r v m -1 v = wr ms w = 2pf rad/sec Typically the Gravitron ride takes approximately 20 seconds to reach its maximum rotational speed of 24 rpms and the whole ride lasts for around 80 seconds. This means the ride’s occupants are exposed to non-uniform circular motion meaning there is changing linear velocity at certain parts of the ride. For non-uniform circular motion the following formulae are useful: where: A GPS tracking device was attached to a person in the Gravitron and data was obtained about their x,y displacement vs. time over the 80 second duration of the ride. The data was saved in a .csv file called ‘gravitron.csv.’ This file contains three columns: time, x-displacement and y-displacement, e.g.: Time, sec x-displacement y-displacement 0.00 0.10 0.20 … 2. Download this .csv file from Blackboard. Find the g-forces being applied to the ride’s occupants for the whole 80 second duration of the ride. Again assume the occupants are 65 kg adults. Think about how you could effectively present these results. -2 2 ms r v -1 a = 2 2 ms     +     = dt dy dt dx v centripetal acceleration time in seconds displacement in y direction displacement in x direction = = = = a t y x

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31. A circuit has a continuous path through which charge can flow from a voltage source to a device that uses electrical energy. What is the name of this type of circuit? a. a short circuit c. an open circuit b. a closed circuit d. a circuit schematic

31. A circuit has a continuous path through which charge can flow from a voltage source to a device that uses electrical energy. What is the name of this type of circuit? a. a short circuit c. an open circuit b. a closed circuit d. a circuit schematic

31. ANS: B PTS: 1 DIF: II OBJ: 18-1.2   … Read More...
Tornado Eddy Investigation Abstract The objective of this lab was to write a bunch of jibberish to provide students with a formatting template. Chemical engineering, bioengineering, and environmental engineering are “process engineering” disciplines. Good abstracts contains real content, such as 560 mL/min, 35 deg, and 67 percent yield. Ideal degreed graduates are technically strong, bring broad system perspectives to problem solving, and have the professional “soft skills” to make immediate contributions in the workplace. The senior lab sequence is the “capstone” opportunity to realize this ideal by integrating technical skills and developing professional soft skills to ensure workforce preparedness. The best conclusions are objective and numerical, such as operating conditions of 45 L/min at 32 deg C with expected costs of $4.55/lb. Background Insect exchange processes are often used in bug filtration, as they are effective at removing either positive or negative insects from water. An insect exchange column is a packed or fluidized bed filled with resin beads. Water flows through the column and most of the insects from the water enter the beads, but some of them pass in between the beads, which makes the exchange of insects non-ideal. Insectac 249 resin is a cation exchange resin, as it is being used to attract cationic Ca2+ from the toxic waste stream. This means the resin is negatively charged, and needs to be regenerated with a solution that produces positively charged insects, in this case, salt water which contains Na+ insects. The resin contains acidic styrene backbones which capture the cationic insects in a reversible process. A curve of Ca2+ concentration concentration vs. time was obtained after a standard curve was made to determine how many drops from the low cost barium test kit from Aquarium Pharmaceuticals (API)1 bottle #2 would correspond to a certain concentration in solution. A standard curve works by preparing solutions with known concentrations and testing these concentrations using the kit to create a curve of number of drops from bottle #2 (obtained result) vs. concentration of Ca2+ in solution (desired response). The standard curve can then be used for every test on the prototype and in the field, to quickly and accurately obtain a concentration from the test kit. The barium concentration vs. time curve can be used to calculate the exchange capacity of the resin and, in later tests, the regeneration efficiency. The curves must be used to get the total amount of barium removed from the water, m. Seen in Equation 2, the volumetric flow rate of water, , is multiplied by the integral from tinitial to tfinal of the total concentration of Ca2+ absorbed by the resin as a function of time, C. (2) 1 http://aquariumpharm.com/Products/Product.aspx?ProductID=72 , date accessed: 11/26/10 CBEE 102: ENGINEERING PROBLEM SOLVING AND COMPUTATIONS PROJECT DESCRIPTION 9 Josephine Hornsnogger CBEE 414, Lab Section M 1300–‐1550 April 19, 2010 Oregon State University School of CBEE A graphical trapezoid method was used to evaluate the integral and get the final solution in equivalents of Ca2+ per L, it must be noted that there are 2 equivalents per mole of barium, as the charge of the barium insect is +2. An initial exchange capacity was calculated for the virgin resin, and an adjusted exchange capacity was calculated once the resin was regenerated. The regenerated resin capacity was found by multiplying the virgin resin capacity by the regeneration efficiency, expressed in Equation 3. (3) See Appendix A for the calculation of the exchange capacities and the regeneration efficiency. Materials and Methods Rosalie and Peter Johnson of Corvallis established the Linus Pauling Chair in Chemical Engineering to honor Oregon State University’s most famous graduate. Peter Johnson, former President and owner of Tekmax, Inc., a company which revolutionized battery manufacturing equipment, is a 1955 graduate of the College of Engineering.2 The Chair, also known as the Linus Pauling Distinguished Engineer or Linus Pauling Engineer (LPE), was originally designed to focus on the traditional “capstone” senior lab sequence in the former Department of Chemical Engineering. The focus is now extended to all the process engineering disciplines. The LPE is charged with establishing strong ties with industry, ensuring current and relevant laboratory experiences, and helping upperclass students develop skills in communication, teamwork, project management, and leadership. Include details about lab procedures not sufficiently detailed in the SOP, problems you had, etc. The bulk solution prepared to create the standard curve was used in the second day of testing to obtain the exchange capacity of the insectac 249 resin. The solution was pumped through a bathroom scale into the prototype insect exchange column. 45 mL of resin was rinsed and added to the column. The bed was fluidized as the solution was pumped through the resin, but for the creation of the Ca2+ concentration vs. time curve, the solution was pumped down through the column, as illustrated in the process flow diagram seen in Figure 1. Figure 1. Process sketch of the insect exchange column used for the project. Ref: http://www.generon.co.uk/acatalog/Chromatography.html 2 Harding, P. Viscosity Measurement SOP, Spring, 2010. CBEE 102: ENGINEERING PROBLEM SOLVING AND COMPUTATIONS PROJECT DESCRIPTION 10 Josephine Hornsnogger CBEE 414, Lab Section M 1300–‐1550 April 19, 2010 Oregon State University School of CBEE A bathroom scale calibration curve was created to ensure that the 150 mL/min, used to calculate the breakthrough time, would be delivered to the resin. The bathroom scale used was a Dwyer brand with flowrates between 0 and 300 cc/min of water. Originally, values between 120 and 180 mL/min were chosen for the calibration, with three runs for each flowrate, however the bathroom scale values were so far away from the measure values the range was extended to 100 to 200 mL/min. The regeneration experiment was performed using a method similar to that used in the water softening experiment, however instead of using a 640 ppm Ca2+ solution to fill the resin, a 6000 ppm Na+ solution was used to eject the Ca2+ from the resin. Twelve samples times were chosen and adjusted as the experiment progressed, with more than half of the samples taken at times less than 10 minutes, and the last sample taken at 45 minutes. The bulk exit solution was also tested to determine the regeneration efficiency. Results and Discussion The senior lab sequence has its roots in the former Department of Chemical Engineering. CHE 414 and 415 were taught in Winter and Spring and included 6 hours of lab time per week. The School has endeavored to incorporate the courses into the BIOE and ENVE curriculum, and this will be complete in 2008-2009. Recent development of the senior lab course sequence is shown chronologically in Fig. 1. In 2006-2007, CHE 414 and 415 were moved to Fall and Winter to enable CHE 416, an elective independent senior project course. Also that year, BIOE students took BIOE 414 in the Fall and BIOE 415 was developed and taught. No BIOE students enrolled in the optional CHE. In 2007-2008, the program transitioned in a new Linus Pauling Engineer and ENVE 414 was offered. Also, approximately 30 percent of BIOE students enrolled in the optional CHE 416. Accommodating the academic calendars of the three disciplines required a reduction in weekly student lab time from 6 to 3 hours. The expected relationship between coughing rate, y, and length of canine, x, is Bx z y Fe− (1) where F is a pre-exponential constant, B is vitamin B concentration and z is the height of an average trapeze artist. 3 The 2008-2009 brings the challenge of the dramatic enrollment increase shown in Fig. 1 and the first offering of ENVE 415. The result, shown on the right in Fig. 1, is the delivery of the senior lab sequence uniformly across the process engineering disciplines. CBEE 416 is expected to drawn approximately of the students that take the 415 courses. In 2007-2008, 414 and 415 were required for CHEs, 414 and 415 for BIOEs, and only 414 for ENVEs. CHE 416 is ostensibly an elective for all disciplines. In 2008-2009, 414 and 415 is required for all disciplines and CHE 416 will be an elective. The content of 414 is essentially 3 Fundamentals of Momentum, Heat, and Mass Transfer, Welty, J.R. et al., 4th edition, John Wiley & Sons, Inc. CBEE 102: ENGINEERING PROBLEM SOLVING AND COMPUTATIONS PROJECT DESCRIPTION 11 Josephine Hornsnogger CBEE 414, Lab Section M 1300–‐1550 April 19, 2010 Oregon State University School of CBEE identical for all three disciplines, 415 has discipline-specific labs, and 416 consists of senior projects with potentially cross-discipline teams of 2 to 4 students. Tremendous labor and struggling with the lab equipment resulted in the data shown in y = –‐0.29x + 1.71 y = –‐0.25x + 2.03 y = –‐0.135x + 2.20 –‐1.5 –‐1.0 –‐0.5 0.0 0.5 1.0 1.5 2.0 2.5 0 2 4 6 8 10 ln y (units) x (units) ln y_1 ln y_2 ln y_3 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Case 1 Case 2 Case 3 Slope (units) (a) (b) Figure 1. (a) Data for y and x plotted for various values of z and (b) a comparison of slopes for the 3 cases investigate. The log plot slope yields the vitamin B concentration. The slopes were shown to be significantly at the 90% confidence level, but the instructor ran out of time and did not include error bars. The slope changed as predicted by the Snirtenhoffer equation. Improvements to the lab might include advice on how to legally change my name to something less embarrassing. My whole life I have been forced to repeat and spell it. I really feel that this has affected my psychologically. This was perhaps the worst lab I have ever done in my academic career, primarily due to the fact that there was no lab time. I simply typed in this entire report and filled it with jibberish. Some might think nobody will notice, but I know that …… Harding reads every word. Acknowledgments The author acknowledges his elementary teacher for providing truly foundational instruction in addition and subtraction. Jenny Burninbalm was instrumental with guidance on use of the RT-345 dog scratching device. CBEE 102: ENGINEERING PROBLEM SOLVING AND COMPUTATIONS PROJECT DESCRIPTION 12

Tornado Eddy Investigation Abstract The objective of this lab was to write a bunch of jibberish to provide students with a formatting template. Chemical engineering, bioengineering, and environmental engineering are “process engineering” disciplines. Good abstracts contains real content, such as 560 mL/min, 35 deg, and 67 percent yield. Ideal degreed graduates are technically strong, bring broad system perspectives to problem solving, and have the professional “soft skills” to make immediate contributions in the workplace. The senior lab sequence is the “capstone” opportunity to realize this ideal by integrating technical skills and developing professional soft skills to ensure workforce preparedness. The best conclusions are objective and numerical, such as operating conditions of 45 L/min at 32 deg C with expected costs of $4.55/lb. Background Insect exchange processes are often used in bug filtration, as they are effective at removing either positive or negative insects from water. An insect exchange column is a packed or fluidized bed filled with resin beads. Water flows through the column and most of the insects from the water enter the beads, but some of them pass in between the beads, which makes the exchange of insects non-ideal. Insectac 249 resin is a cation exchange resin, as it is being used to attract cationic Ca2+ from the toxic waste stream. This means the resin is negatively charged, and needs to be regenerated with a solution that produces positively charged insects, in this case, salt water which contains Na+ insects. The resin contains acidic styrene backbones which capture the cationic insects in a reversible process. A curve of Ca2+ concentration concentration vs. time was obtained after a standard curve was made to determine how many drops from the low cost barium test kit from Aquarium Pharmaceuticals (API)1 bottle #2 would correspond to a certain concentration in solution. A standard curve works by preparing solutions with known concentrations and testing these concentrations using the kit to create a curve of number of drops from bottle #2 (obtained result) vs. concentration of Ca2+ in solution (desired response). The standard curve can then be used for every test on the prototype and in the field, to quickly and accurately obtain a concentration from the test kit. The barium concentration vs. time curve can be used to calculate the exchange capacity of the resin and, in later tests, the regeneration efficiency. The curves must be used to get the total amount of barium removed from the water, m. Seen in Equation 2, the volumetric flow rate of water, , is multiplied by the integral from tinitial to tfinal of the total concentration of Ca2+ absorbed by the resin as a function of time, C. (2) 1 http://aquariumpharm.com/Products/Product.aspx?ProductID=72 , date accessed: 11/26/10 CBEE 102: ENGINEERING PROBLEM SOLVING AND COMPUTATIONS PROJECT DESCRIPTION 9 Josephine Hornsnogger CBEE 414, Lab Section M 1300–‐1550 April 19, 2010 Oregon State University School of CBEE A graphical trapezoid method was used to evaluate the integral and get the final solution in equivalents of Ca2+ per L, it must be noted that there are 2 equivalents per mole of barium, as the charge of the barium insect is +2. An initial exchange capacity was calculated for the virgin resin, and an adjusted exchange capacity was calculated once the resin was regenerated. The regenerated resin capacity was found by multiplying the virgin resin capacity by the regeneration efficiency, expressed in Equation 3. (3) See Appendix A for the calculation of the exchange capacities and the regeneration efficiency. Materials and Methods Rosalie and Peter Johnson of Corvallis established the Linus Pauling Chair in Chemical Engineering to honor Oregon State University’s most famous graduate. Peter Johnson, former President and owner of Tekmax, Inc., a company which revolutionized battery manufacturing equipment, is a 1955 graduate of the College of Engineering.2 The Chair, also known as the Linus Pauling Distinguished Engineer or Linus Pauling Engineer (LPE), was originally designed to focus on the traditional “capstone” senior lab sequence in the former Department of Chemical Engineering. The focus is now extended to all the process engineering disciplines. The LPE is charged with establishing strong ties with industry, ensuring current and relevant laboratory experiences, and helping upperclass students develop skills in communication, teamwork, project management, and leadership. Include details about lab procedures not sufficiently detailed in the SOP, problems you had, etc. The bulk solution prepared to create the standard curve was used in the second day of testing to obtain the exchange capacity of the insectac 249 resin. The solution was pumped through a bathroom scale into the prototype insect exchange column. 45 mL of resin was rinsed and added to the column. The bed was fluidized as the solution was pumped through the resin, but for the creation of the Ca2+ concentration vs. time curve, the solution was pumped down through the column, as illustrated in the process flow diagram seen in Figure 1. Figure 1. Process sketch of the insect exchange column used for the project. Ref: http://www.generon.co.uk/acatalog/Chromatography.html 2 Harding, P. Viscosity Measurement SOP, Spring, 2010. CBEE 102: ENGINEERING PROBLEM SOLVING AND COMPUTATIONS PROJECT DESCRIPTION 10 Josephine Hornsnogger CBEE 414, Lab Section M 1300–‐1550 April 19, 2010 Oregon State University School of CBEE A bathroom scale calibration curve was created to ensure that the 150 mL/min, used to calculate the breakthrough time, would be delivered to the resin. The bathroom scale used was a Dwyer brand with flowrates between 0 and 300 cc/min of water. Originally, values between 120 and 180 mL/min were chosen for the calibration, with three runs for each flowrate, however the bathroom scale values were so far away from the measure values the range was extended to 100 to 200 mL/min. The regeneration experiment was performed using a method similar to that used in the water softening experiment, however instead of using a 640 ppm Ca2+ solution to fill the resin, a 6000 ppm Na+ solution was used to eject the Ca2+ from the resin. Twelve samples times were chosen and adjusted as the experiment progressed, with more than half of the samples taken at times less than 10 minutes, and the last sample taken at 45 minutes. The bulk exit solution was also tested to determine the regeneration efficiency. Results and Discussion The senior lab sequence has its roots in the former Department of Chemical Engineering. CHE 414 and 415 were taught in Winter and Spring and included 6 hours of lab time per week. The School has endeavored to incorporate the courses into the BIOE and ENVE curriculum, and this will be complete in 2008-2009. Recent development of the senior lab course sequence is shown chronologically in Fig. 1. In 2006-2007, CHE 414 and 415 were moved to Fall and Winter to enable CHE 416, an elective independent senior project course. Also that year, BIOE students took BIOE 414 in the Fall and BIOE 415 was developed and taught. No BIOE students enrolled in the optional CHE. In 2007-2008, the program transitioned in a new Linus Pauling Engineer and ENVE 414 was offered. Also, approximately 30 percent of BIOE students enrolled in the optional CHE 416. Accommodating the academic calendars of the three disciplines required a reduction in weekly student lab time from 6 to 3 hours. The expected relationship between coughing rate, y, and length of canine, x, is Bx z y Fe− (1) where F is a pre-exponential constant, B is vitamin B concentration and z is the height of an average trapeze artist. 3 The 2008-2009 brings the challenge of the dramatic enrollment increase shown in Fig. 1 and the first offering of ENVE 415. The result, shown on the right in Fig. 1, is the delivery of the senior lab sequence uniformly across the process engineering disciplines. CBEE 416 is expected to drawn approximately of the students that take the 415 courses. In 2007-2008, 414 and 415 were required for CHEs, 414 and 415 for BIOEs, and only 414 for ENVEs. CHE 416 is ostensibly an elective for all disciplines. In 2008-2009, 414 and 415 is required for all disciplines and CHE 416 will be an elective. The content of 414 is essentially 3 Fundamentals of Momentum, Heat, and Mass Transfer, Welty, J.R. et al., 4th edition, John Wiley & Sons, Inc. CBEE 102: ENGINEERING PROBLEM SOLVING AND COMPUTATIONS PROJECT DESCRIPTION 11 Josephine Hornsnogger CBEE 414, Lab Section M 1300–‐1550 April 19, 2010 Oregon State University School of CBEE identical for all three disciplines, 415 has discipline-specific labs, and 416 consists of senior projects with potentially cross-discipline teams of 2 to 4 students. Tremendous labor and struggling with the lab equipment resulted in the data shown in y = –‐0.29x + 1.71 y = –‐0.25x + 2.03 y = –‐0.135x + 2.20 –‐1.5 –‐1.0 –‐0.5 0.0 0.5 1.0 1.5 2.0 2.5 0 2 4 6 8 10 ln y (units) x (units) ln y_1 ln y_2 ln y_3 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Case 1 Case 2 Case 3 Slope (units) (a) (b) Figure 1. (a) Data for y and x plotted for various values of z and (b) a comparison of slopes for the 3 cases investigate. The log plot slope yields the vitamin B concentration. The slopes were shown to be significantly at the 90% confidence level, but the instructor ran out of time and did not include error bars. The slope changed as predicted by the Snirtenhoffer equation. Improvements to the lab might include advice on how to legally change my name to something less embarrassing. My whole life I have been forced to repeat and spell it. I really feel that this has affected my psychologically. This was perhaps the worst lab I have ever done in my academic career, primarily due to the fact that there was no lab time. I simply typed in this entire report and filled it with jibberish. Some might think nobody will notice, but I know that …… Harding reads every word. Acknowledgments The author acknowledges his elementary teacher for providing truly foundational instruction in addition and subtraction. Jenny Burninbalm was instrumental with guidance on use of the RT-345 dog scratching device. CBEE 102: ENGINEERING PROBLEM SOLVING AND COMPUTATIONS PROJECT DESCRIPTION 12

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1. Express in your own words the meaning of these terms a. Indicator b. Acid-base indicator c. Hydronium ion Acidic solution Basic/alkaline solution Salt d. Neutralization reaction Acid e. Base f. Acid-base reaction Strong acid g. Weak acid h. Strong base i. Weak base j. Molarity k. pH l. Neutral m. Buffer

1. Express in your own words the meaning of these terms a. Indicator b. Acid-base indicator c. Hydronium ion Acidic solution Basic/alkaline solution Salt d. Neutralization reaction Acid e. Base f. Acid-base reaction Strong acid g. Weak acid h. Strong base i. Weak base j. Molarity k. pH l. Neutral m. Buffer

Express in your own words the meaning of these terms: … Read More...
1 Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 3.1 Laboratory Objective The objective of this laboratory is to understand the basic properties of sinusoids and sinusoid measurements. 3.2 Educational Objectives After performing this experiment, students should be able to: 1. Understand the properties of sinusoids. 2. Understand sinusoidal manipulation 3. Use a function generator 4. Obtain measurements using an oscilloscope 3.3 Background Sinusoids are sine or cosine waveforms that can describe many engineering phenomena. Any oscillatory motion can be described using sinusoids. Many types of electrical signals such as square, triangle, and sawtooth waves are modeled using sinusoids. Their manipulation incurs the understanding of certain quantities that describe sinusoidal behavior. These quantities are described below. 3.3.1 Sinusoid Characteristics Amplitude The amplitude A of a sine wave describes the height of the hills and valleys of a sinusoid. It carries the physical units of what the sinusoid is describing (volts, amps, meters, etc.). Frequency There are two types of frequencies that can describe a sinusoid. The normal frequency f is how many times the sinusoid repeats per unit time. It has units of cycles per second (s-1) or Hertz (Hz). The angular frequency ω is how many radians pass per second. Consequently, ω has units of radians per second. Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 2 Period The period T is how long a sinusoid takes to repeat one complete cycle. The period is measured in seconds. Phase The phase φ of a sinusoid causes a horizontal shift along the t-axis. The phase has units of radians. TimeShift The time shift ts of a sinusoid is a horizontal shift along the t-axis and is a time measurement of the phase. The time shift has units of seconds. NOTE: A sine wave and a cosine wave only differ by a phase shift of 90° or ?2 radians. In reality, they are the same waveform but with a different φ value. 3.3.2 Sinusoidal Relationships Figure 3.1: Sinusoid The general equation of a sinusoid is given below and refers to Figure 3.1. ?(?) = ????(?? +?) (3.1) The angular frequency is related to the normal frequency by Equation 3.2. ?= 2?? (3.2) The angular frequency is also related to the period by Equation 3.3. ?=2?? (3.3) By inspection, the normal frequency is related to the period by Equation 3.4. ? =1? (3.4) ?? Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 3 The time shift is related to the phase (radians) and the frequency by Equation 3.5. ??= ∅2?? (3.5) 3.3.3 Equipment 3.3.3.1 Inductors Inductors are electrical components that resist a change in the flow of current passing through them. They are essentially coils of wire. Inductors are electromagnets too. They are represented in schematics using the following symbol and physically using the following equipment (with or without exposed wire): Figure 3.2: Symbol and Physical Example for Inductors 3.3.3.2 Capacitors Capacitors are electrical components that store energy. This enables engineers to store electrical energy from an input source such as a battery. Some capacitors are polarized and therefore have a negative and positive plate. One plate is straight, representing the positive terminal on the device, and the other is curved, representing the negative one. Polarized capacitors are represented in schematics using the following symbol and physically using the following equipment: Figure 3.3: Symbol and Physical Example for Capacitors 3.3.3.3 Function Generator A function generator is used to create different types of electrical waveforms over a wide range of frequencies. It generates standard sine, square, and triangle waveforms and uses the analog output channel. 3.3.3.5 Oscilloscope An oscilloscope is a type of electronic test instrument that allows observation of constantly varying voltages, usually as a two-dimensional plot of one or more signals as a function of time. It displays voltage data over time for the analysis of one or two voltage measurements taken from the analog input channels of the Oscilloscope. The observed waveform can be analyzed for amplitude, frequency, time interval and more. Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 4 3.4 Procedure Follow the steps outlined below after the instructor has explained how to use the laboratory equipment 3.4.1 Sinusoidal Measurements 1. Connect the output channel of the Function Generator to the channel one of the Oscilloscope. 2. Complete Table 3.1 using the given values for voltage and frequency. Table 3.1: Sinusoid Measurements Function Generator Oscilloscope (Measured) Calculated Voltage Amplitude, A (V ) Frequency (Hz) 2*A (Vp−p ) f (Hz) T (sec) ω (rad/sec) T (sec) 2.5 1000 3 5000 3.4.2 Circuit Measurements 1. Connect the circuit in figure 3.4 below with the given resistor and capacitor NOTE: Vs from the circuit comes from the Function Generator using a BNC connector. Figure 3.4: RC Circuit Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 5 2. Using the alligator to BNC cables, connect channel one of the Oscilloscope across the capacitor and complete Table 3.2 Table 3.2: Capacitor Sinusoid Function Generator Oscilloscope (Measured) Calculated Vs (Volts) Frequency (Hz) Vc (volts) f (Hz) T (sec) ω (rad/sec) 2.5 100 3. Disconnect channel one and connect channel two of the oscilloscope across the resistor and complete table 3.3. Table 3.3: Resistor Sinusoid Function Generator Oscilloscope (Measured) Calculated Vs (Volts) Frequency (Hz) VR (volts) f (Hz) T (sec) ω (rad/sec) 2.5 100 4. Leaving channel two connected across the resistor, clip the positive lead to the positive side of the capacitor and complete table 3.4 Table 3.4: Phase Difference Function Generator Oscilloscope (Measured) Calculated Vs (volts) Frequency (Hz) Divisions Time/Div (sec) ts (sec) ɸ (rad) ɸ (degrees) 2.5 100 5. Using the data from Tables 3.2, 3.3, and 3.4, plot the capacitor sinusoidal equation and the resistor sinusoidal equation on the same graph using MATLAB. HINT: Plot over one period. 6. Kirchoff’s Voltage Law states that ??(?)=??(?)+??(?). Calculate Vs by hand using the following equation and Tables 3.2 and 3.3 ??(?)=√??2+??2???(??−???−1(????)) Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 6 3.5 New MATLAB Commands hold on  This command allows multiple graphs to be placed on the same XY axis and is placed after the first plot statement. legend (’string 1’, ’string2’, ‘string3’)  This command adds a legend to the plot. Strings must be placed in the order as the plots were generated. plot (x, y, ‘line specifiers’)  This command plots the data and uses line specifiers to differentiate between different plots on the same XY axis. In this lab, only use different line styles from the table below. Table 3.5: Line specifiers for the plot() command sqrt(X)  This command produces the square root of the elements of X. NOTE: The “help” command in MATLAB can be used to find a description and example for functions such as input.  For example, type “help input” in the command window to learn more about the input function. NOTE: Refer to section the “MATLAB Commands” sections from prior labs for previously discussed material that you may also need in order to complete this assignment. Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 7 3.6 Lab Report Requirements 1. Complete Tables 3.1, 3.2, 3.3, 3.4 (5 points each) 2. Show hand calculations for all four tables. Insert after this page (5 points each) 3. Draw the two sinusoids by hand from table 3.1. Label amplitude, period, and phase. Insert after this page. (5 points) 4. Insert MATLAB plot of Vc and VR as obtained from data in Tables 3.2 and 3.3 after this page. (5 points each) 5. Show hand calculations for Vs(t). Insert after this page. (5 points) 6. Using the data from the Tables, write: (10 points) a) Vc(t) = b) VR(t) = 7. Also, ???(?)=2.5???(628?). Write your Vs below and give reasons why they are different. (10 points) a) Vs(t) = b) Reasons: 8. Write an executive summary for this lab describing what you have done, and learned. (20 points)

1 Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 3.1 Laboratory Objective The objective of this laboratory is to understand the basic properties of sinusoids and sinusoid measurements. 3.2 Educational Objectives After performing this experiment, students should be able to: 1. Understand the properties of sinusoids. 2. Understand sinusoidal manipulation 3. Use a function generator 4. Obtain measurements using an oscilloscope 3.3 Background Sinusoids are sine or cosine waveforms that can describe many engineering phenomena. Any oscillatory motion can be described using sinusoids. Many types of electrical signals such as square, triangle, and sawtooth waves are modeled using sinusoids. Their manipulation incurs the understanding of certain quantities that describe sinusoidal behavior. These quantities are described below. 3.3.1 Sinusoid Characteristics Amplitude The amplitude A of a sine wave describes the height of the hills and valleys of a sinusoid. It carries the physical units of what the sinusoid is describing (volts, amps, meters, etc.). Frequency There are two types of frequencies that can describe a sinusoid. The normal frequency f is how many times the sinusoid repeats per unit time. It has units of cycles per second (s-1) or Hertz (Hz). The angular frequency ω is how many radians pass per second. Consequently, ω has units of radians per second. Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 2 Period The period T is how long a sinusoid takes to repeat one complete cycle. The period is measured in seconds. Phase The phase φ of a sinusoid causes a horizontal shift along the t-axis. The phase has units of radians. TimeShift The time shift ts of a sinusoid is a horizontal shift along the t-axis and is a time measurement of the phase. The time shift has units of seconds. NOTE: A sine wave and a cosine wave only differ by a phase shift of 90° or ?2 radians. In reality, they are the same waveform but with a different φ value. 3.3.2 Sinusoidal Relationships Figure 3.1: Sinusoid The general equation of a sinusoid is given below and refers to Figure 3.1. ?(?) = ????(?? +?) (3.1) The angular frequency is related to the normal frequency by Equation 3.2. ?= 2?? (3.2) The angular frequency is also related to the period by Equation 3.3. ?=2?? (3.3) By inspection, the normal frequency is related to the period by Equation 3.4. ? =1? (3.4) ?? Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 3 The time shift is related to the phase (radians) and the frequency by Equation 3.5. ??= ∅2?? (3.5) 3.3.3 Equipment 3.3.3.1 Inductors Inductors are electrical components that resist a change in the flow of current passing through them. They are essentially coils of wire. Inductors are electromagnets too. They are represented in schematics using the following symbol and physically using the following equipment (with or without exposed wire): Figure 3.2: Symbol and Physical Example for Inductors 3.3.3.2 Capacitors Capacitors are electrical components that store energy. This enables engineers to store electrical energy from an input source such as a battery. Some capacitors are polarized and therefore have a negative and positive plate. One plate is straight, representing the positive terminal on the device, and the other is curved, representing the negative one. Polarized capacitors are represented in schematics using the following symbol and physically using the following equipment: Figure 3.3: Symbol and Physical Example for Capacitors 3.3.3.3 Function Generator A function generator is used to create different types of electrical waveforms over a wide range of frequencies. It generates standard sine, square, and triangle waveforms and uses the analog output channel. 3.3.3.5 Oscilloscope An oscilloscope is a type of electronic test instrument that allows observation of constantly varying voltages, usually as a two-dimensional plot of one or more signals as a function of time. It displays voltage data over time for the analysis of one or two voltage measurements taken from the analog input channels of the Oscilloscope. The observed waveform can be analyzed for amplitude, frequency, time interval and more. Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 4 3.4 Procedure Follow the steps outlined below after the instructor has explained how to use the laboratory equipment 3.4.1 Sinusoidal Measurements 1. Connect the output channel of the Function Generator to the channel one of the Oscilloscope. 2. Complete Table 3.1 using the given values for voltage and frequency. Table 3.1: Sinusoid Measurements Function Generator Oscilloscope (Measured) Calculated Voltage Amplitude, A (V ) Frequency (Hz) 2*A (Vp−p ) f (Hz) T (sec) ω (rad/sec) T (sec) 2.5 1000 3 5000 3.4.2 Circuit Measurements 1. Connect the circuit in figure 3.4 below with the given resistor and capacitor NOTE: Vs from the circuit comes from the Function Generator using a BNC connector. Figure 3.4: RC Circuit Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 5 2. Using the alligator to BNC cables, connect channel one of the Oscilloscope across the capacitor and complete Table 3.2 Table 3.2: Capacitor Sinusoid Function Generator Oscilloscope (Measured) Calculated Vs (Volts) Frequency (Hz) Vc (volts) f (Hz) T (sec) ω (rad/sec) 2.5 100 3. Disconnect channel one and connect channel two of the oscilloscope across the resistor and complete table 3.3. Table 3.3: Resistor Sinusoid Function Generator Oscilloscope (Measured) Calculated Vs (Volts) Frequency (Hz) VR (volts) f (Hz) T (sec) ω (rad/sec) 2.5 100 4. Leaving channel two connected across the resistor, clip the positive lead to the positive side of the capacitor and complete table 3.4 Table 3.4: Phase Difference Function Generator Oscilloscope (Measured) Calculated Vs (volts) Frequency (Hz) Divisions Time/Div (sec) ts (sec) ɸ (rad) ɸ (degrees) 2.5 100 5. Using the data from Tables 3.2, 3.3, and 3.4, plot the capacitor sinusoidal equation and the resistor sinusoidal equation on the same graph using MATLAB. HINT: Plot over one period. 6. Kirchoff’s Voltage Law states that ??(?)=??(?)+??(?). Calculate Vs by hand using the following equation and Tables 3.2 and 3.3 ??(?)=√??2+??2???(??−???−1(????)) Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 6 3.5 New MATLAB Commands hold on  This command allows multiple graphs to be placed on the same XY axis and is placed after the first plot statement. legend (’string 1’, ’string2’, ‘string3’)  This command adds a legend to the plot. Strings must be placed in the order as the plots were generated. plot (x, y, ‘line specifiers’)  This command plots the data and uses line specifiers to differentiate between different plots on the same XY axis. In this lab, only use different line styles from the table below. Table 3.5: Line specifiers for the plot() command sqrt(X)  This command produces the square root of the elements of X. NOTE: The “help” command in MATLAB can be used to find a description and example for functions such as input.  For example, type “help input” in the command window to learn more about the input function. NOTE: Refer to section the “MATLAB Commands” sections from prior labs for previously discussed material that you may also need in order to complete this assignment. Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 7 3.6 Lab Report Requirements 1. Complete Tables 3.1, 3.2, 3.3, 3.4 (5 points each) 2. Show hand calculations for all four tables. Insert after this page (5 points each) 3. Draw the two sinusoids by hand from table 3.1. Label amplitude, period, and phase. Insert after this page. (5 points) 4. Insert MATLAB plot of Vc and VR as obtained from data in Tables 3.2 and 3.3 after this page. (5 points each) 5. Show hand calculations for Vs(t). Insert after this page. (5 points) 6. Using the data from the Tables, write: (10 points) a) Vc(t) = b) VR(t) = 7. Also, ???(?)=2.5???(628?). Write your Vs below and give reasons why they are different. (10 points) a) Vs(t) = b) Reasons: 8. Write an executive summary for this lab describing what you have done, and learned. (20 points)

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Scenario: You are to design synchronous and asynchronous circuits that will allow the following requirements to be met. Tasks: 1. Packet number checking A synchronous sequential machine is to have a single input line and a single output line. The circuit is to receive messages of 4-bit words coded in binary (least significant bit first). The purpose of the circuit is to detect whether the number coming in is a prime number (divisible by only itself and 1). Thus, the output is to become 1 whenever a 4-bit word does represent a valid prime number. At the end of each word the machine is to return to the reset starting state. Steps: 1) Draw a State Diagram (Mealy) and check for redundancies 2) Then assign binary State Identifiers. 3) Make a Next State Truth Table (NSTT) 4) Select a bistable type 5) Determine expressions for the bistable inputs 6) Determine expressions for the outputs 2. Monitoring System A monitoring system sends 1s positive going pulses to a device to ensure that it is operating correctly. The device will respond by lowering its normally high line as soon as it receives the pulse then raising the line again within the 1s if working correctly. If the device line doesn’t respond correctly or respond at all then an alarm must occur. 1) Carry out a design for the asynchronous system that will realise the requirements up to the point where internal conditions are designated to the lines in the merged table. 2) Explain what the designer would have to do to ensure the system was hazard free and the output was as short as possible.

Scenario: You are to design synchronous and asynchronous circuits that will allow the following requirements to be met. Tasks: 1. Packet number checking A synchronous sequential machine is to have a single input line and a single output line. The circuit is to receive messages of 4-bit words coded in binary (least significant bit first). The purpose of the circuit is to detect whether the number coming in is a prime number (divisible by only itself and 1). Thus, the output is to become 1 whenever a 4-bit word does represent a valid prime number. At the end of each word the machine is to return to the reset starting state. Steps: 1) Draw a State Diagram (Mealy) and check for redundancies 2) Then assign binary State Identifiers. 3) Make a Next State Truth Table (NSTT) 4) Select a bistable type 5) Determine expressions for the bistable inputs 6) Determine expressions for the outputs 2. Monitoring System A monitoring system sends 1s positive going pulses to a device to ensure that it is operating correctly. The device will respond by lowering its normally high line as soon as it receives the pulse then raising the line again within the 1s if working correctly. If the device line doesn’t respond correctly or respond at all then an alarm must occur. 1) Carry out a design for the asynchronous system that will realise the requirements up to the point where internal conditions are designated to the lines in the merged table. 2) Explain what the designer would have to do to ensure the system was hazard free and the output was as short as possible.

Scenario: You are to design synchronous and asynchronous circuits that … Read More...
The life X, in hours, of a certain device, has a pdf fX(t) = ( 100 y2 ; t  100 0; t < 100 (a) What are the probability that this device will survive 250 hours of operation? (b) Find the life expectancy of the device.

The life X, in hours, of a certain device, has a pdf fX(t) = ( 100 y2 ; t  100 0; t < 100 (a) What are the probability that this device will survive 250 hours of operation? (b) Find the life expectancy of the device.

For any additional help, please contact: info@checkyourstudy.com Call and Whatsapp … Read More...
MAE 318: System Dynamics and Control Dr. Panagiotis K. Artemiadis MAE 318: System Dynamics and Control Homework 4 Problem 1: (Points: 25) The circuit shown in Fig. 1 is excited by an impulse of 0.015V. Assuming the capacitor is initially discharged, obtain an analytic expression of vO (t), and make a Matlab program that plots the system response to the impulse. Figure 1 Problem 2: Extra Credit (Points: 25) A winding oscillator consists of two steel spheres on each end of a long slender rod, as shown in Fig. 2. The rod is hung on a thin wire that can be twisted many revolutions without breaking. The device will be wound up 4000 degrees. Make a Matlab script that computes the system response and determine how long will it take until the motion decays to a swing of only 10 degrees? Assume that the thin wire has a rotational spring constant of 2  10?4Nm/rad and that the viscous friction coecient for the sphere in air is 2  10?4Nms/rad. Each sphere has a mass of 1Kg. Figure 2: Winding oscillator. Problem 3: (Points: 25) Find the equivalent transfer function T (s) = C(s) R(s) for the system shown in Fig. 3. Arizona State University. Fall 2015. Class # 73024. MAE 318. Homework 4: Page 1 of 4 MAE 318: System Dynamics and Control Dr. Panagiotis K. Artemiadis Figure 3 Problem 4: (Points: 25) Reduce the block diagram shown in Fig. 4 to a single transfer function T (s) = C(s) R(s) . Figure 4 Problem 5: (Points: 25) Consider the rotational mechanical system shown in Fig. 5. Represent the system as a block diagram. Arizona State University. Fall 2015. Class # 73024. MAE 318. Homework 4: Page 2 of 4 MAE 318: System Dynamics and Control Dr. Panagiotis K. Artemiadis Figure 5 Problem 6: (Points: 25) During ascent the space shuttle is steered by commands generated by the computer’s guidance calcu- lations. These commands are in the form of vehicle attitude, attitude rates, and attitude accelerations obtained through measurements made by the vehicle’s inertial measuring unit, rate gyro assembly, and accelerometer assembly, respectively. The ascent digital autopilot uses the errors between the actual and commanded attitude, rates, and accelerations to gimbal the space shuttle main engines (called thrust vectoring) and the solid rocket boosters to a ect the desired vehicle attitude. The space shut- tle’s attitude control system employs the same method in the pitch, roll, and yaw control systems. A simpli ed model of the pitch control system is shown in Fig. 6.  a) Find the closed-loop transfer function relating the actual pitch to commanded pitch. Assume all other inputs are zero.  b) Find the closed-loop transfer function relating the actual pitch rate to commanded pitch rate. Assume all other inputs are zero.  c) Find the closed-loop transfer function relating the actual pitch acceleration to commanded pitch acceleration. Assume all other inputs are zero. Figure 6: Space shuttle pitch control system (simpli ed). Arizona State University. Fall 2015. Class # 73024. MAE 318. Homework 4: Page 3 of 4 MAE 318: System Dynamics and Control Dr. Panagiotis K. Artemiadis Problem 7: (Extra Credit Points: 25) Extenders are robot manipulators that extend (i.e. increase) the strength of the human arm in load- maneuvering tasks (see Fig. 7). The system is represented by the transfer function Y (s) U(s) = G(s) = 30 s2+4s+3 where U (s) is the force of the human hand applied to the robot manipulator, and Y (s) is the force of the robot manipulator applied to the load. Assuming that the force of the human hand that is applied is given by u (t) = 5 sin (!t), create a MATLAB code that will compute and plot the di erence in magnitude and phase between the applied human force and the force of the robot manipulator applied to the load, as a function of the frequency !. Use 100 values for ! in the range ! 2 [0:01; 100] rad s for your two plots. See Fig. 8 on how to de ne di erence in magnitude and phase between two signals. You need to include your code and the two resulted plots in your solution. Figure 7: Human extender. A B dt T: signal period magnitude difference phase difference B A Figure 8: Magnitude and phase di erence (deg) between two sinusoidal signals.

MAE 318: System Dynamics and Control Dr. Panagiotis K. Artemiadis MAE 318: System Dynamics and Control Homework 4 Problem 1: (Points: 25) The circuit shown in Fig. 1 is excited by an impulse of 0.015V. Assuming the capacitor is initially discharged, obtain an analytic expression of vO (t), and make a Matlab program that plots the system response to the impulse. Figure 1 Problem 2: Extra Credit (Points: 25) A winding oscillator consists of two steel spheres on each end of a long slender rod, as shown in Fig. 2. The rod is hung on a thin wire that can be twisted many revolutions without breaking. The device will be wound up 4000 degrees. Make a Matlab script that computes the system response and determine how long will it take until the motion decays to a swing of only 10 degrees? Assume that the thin wire has a rotational spring constant of 2  10?4Nm/rad and that the viscous friction coecient for the sphere in air is 2  10?4Nms/rad. Each sphere has a mass of 1Kg. Figure 2: Winding oscillator. Problem 3: (Points: 25) Find the equivalent transfer function T (s) = C(s) R(s) for the system shown in Fig. 3. Arizona State University. Fall 2015. Class # 73024. MAE 318. Homework 4: Page 1 of 4 MAE 318: System Dynamics and Control Dr. Panagiotis K. Artemiadis Figure 3 Problem 4: (Points: 25) Reduce the block diagram shown in Fig. 4 to a single transfer function T (s) = C(s) R(s) . Figure 4 Problem 5: (Points: 25) Consider the rotational mechanical system shown in Fig. 5. Represent the system as a block diagram. Arizona State University. Fall 2015. Class # 73024. MAE 318. Homework 4: Page 2 of 4 MAE 318: System Dynamics and Control Dr. Panagiotis K. Artemiadis Figure 5 Problem 6: (Points: 25) During ascent the space shuttle is steered by commands generated by the computer’s guidance calcu- lations. These commands are in the form of vehicle attitude, attitude rates, and attitude accelerations obtained through measurements made by the vehicle’s inertial measuring unit, rate gyro assembly, and accelerometer assembly, respectively. The ascent digital autopilot uses the errors between the actual and commanded attitude, rates, and accelerations to gimbal the space shuttle main engines (called thrust vectoring) and the solid rocket boosters to a ect the desired vehicle attitude. The space shut- tle’s attitude control system employs the same method in the pitch, roll, and yaw control systems. A simpli ed model of the pitch control system is shown in Fig. 6.  a) Find the closed-loop transfer function relating the actual pitch to commanded pitch. Assume all other inputs are zero.  b) Find the closed-loop transfer function relating the actual pitch rate to commanded pitch rate. Assume all other inputs are zero.  c) Find the closed-loop transfer function relating the actual pitch acceleration to commanded pitch acceleration. Assume all other inputs are zero. Figure 6: Space shuttle pitch control system (simpli ed). Arizona State University. Fall 2015. Class # 73024. MAE 318. Homework 4: Page 3 of 4 MAE 318: System Dynamics and Control Dr. Panagiotis K. Artemiadis Problem 7: (Extra Credit Points: 25) Extenders are robot manipulators that extend (i.e. increase) the strength of the human arm in load- maneuvering tasks (see Fig. 7). The system is represented by the transfer function Y (s) U(s) = G(s) = 30 s2+4s+3 where U (s) is the force of the human hand applied to the robot manipulator, and Y (s) is the force of the robot manipulator applied to the load. Assuming that the force of the human hand that is applied is given by u (t) = 5 sin (!t), create a MATLAB code that will compute and plot the di erence in magnitude and phase between the applied human force and the force of the robot manipulator applied to the load, as a function of the frequency !. Use 100 values for ! in the range ! 2 [0:01; 100] rad s for your two plots. See Fig. 8 on how to de ne di erence in magnitude and phase between two signals. You need to include your code and the two resulted plots in your solution. Figure 7: Human extender. A B dt T: signal period magnitude difference phase difference B A Figure 8: Magnitude and phase di erence (deg) between two sinusoidal signals.

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