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PHSX 220 Homework 13 Paper – Due Online April 28 – 5:00 pm SHM and Wave the Equation Problem 1: A hanging mass system with a mass of 85 kg, spring constant of k= 490 N/m is realeased from rest from a distance of 10 meters below the systems equilibrium position (similar values to the bottom of a bungee jump). Calculate the following quantities in regards to this system after being released at t=0: a) The angular frequency of the system (radians/sec) b) The frequency of oscillations for the system (Hz) c) The period of oscillations for the system (seconds) d) The time it takes to get back to the equilibrium position of the system for the rst time Problem 2: A horizontal spring-mass system (mass of 2:21×10􀀀25 kg) with no friction has an ocsillation frequency of 9,192,631,770 cycles per second. (a second is de ned by 9,192,631,770 cycles of a Cs-133 atom)). Calculate the e ective spring constant of the system Problem 3: A swinging person, such as Tarzan, can be modeled after a simple pendulum with a mass of 85 kg and a length of 10 m. Consider the mass being released from rest at t=0 at an angle of +15 degrees from the vertical. Calculate the following quantities in regards to this system. You need to be in radians mode for this problem a) The angular frequency of the system (radians/sec) b) The frequency of oscillations for the system in (Hz) c) The period of oscillations of the system (seconds) d) Sketch plots of the angular position, angular velocity and angular acceleration of the system as a function of time. Hint: These will always help you with these time to it takes to a certain point in it’s cycle questions. e) The time it takes for the mass to get half way through its rst cycle (or to the other side of the swing if you were interested in timing say a rescue e ort or something along those lines) . f) The maximum angular velocity of the mass g) The maximum angular accleration of the mass h) The magnitude of the angular momentum of the mass at 3 seconds i) The magnitude of the torque acting on the mass at 3 seconds Problem 4: A wave has a wavenumber of 1 m-1, and an angular frequency of 2 radians per second, travels in the +x direction and has a maximum transverse amplitude of 0.1 m. At t=0, and x =0 the y position is equal to 0.0 m (y(0,0) = 0.0 m). a) Calculate the wavelength of the wave b) Calculate the period of oscillations for the wave c) Calculate the wave speed along the x axis d) Calculate the magnitude and direction of the transverse position of the wave at x=0.5 m and t = 8s e) Calculate the magnitude and direction of the transverse velocity of the wave at x=0.5 m and t = 8s f) Calculate the magnitude and direction of the transverse acceleration of the wave at x=0.5 m and t = 8s Problem 5-6: Chapter 16 Problem 10, 22 Additional Suggested Problems with Solutions Provided: Chapter 16 Problems 5, 9, 15, 45

## PHSX 220 Homework 13 Paper – Due Online April 28 – 5:00 pm SHM and Wave the Equation Problem 1: A hanging mass system with a mass of 85 kg, spring constant of k= 490 N/m is realeased from rest from a distance of 10 meters below the systems equilibrium position (similar values to the bottom of a bungee jump). Calculate the following quantities in regards to this system after being released at t=0: a) The angular frequency of the system (radians/sec) b) The frequency of oscillations for the system (Hz) c) The period of oscillations for the system (seconds) d) The time it takes to get back to the equilibrium position of the system for the rst time Problem 2: A horizontal spring-mass system (mass of 2:21×10􀀀25 kg) with no friction has an ocsillation frequency of 9,192,631,770 cycles per second. (a second is de ned by 9,192,631,770 cycles of a Cs-133 atom)). Calculate the e ective spring constant of the system Problem 3: A swinging person, such as Tarzan, can be modeled after a simple pendulum with a mass of 85 kg and a length of 10 m. Consider the mass being released from rest at t=0 at an angle of +15 degrees from the vertical. Calculate the following quantities in regards to this system. You need to be in radians mode for this problem a) The angular frequency of the system (radians/sec) b) The frequency of oscillations for the system in (Hz) c) The period of oscillations of the system (seconds) d) Sketch plots of the angular position, angular velocity and angular acceleration of the system as a function of time. Hint: These will always help you with these time to it takes to a certain point in it’s cycle questions. e) The time it takes for the mass to get half way through its rst cycle (or to the other side of the swing if you were interested in timing say a rescue e ort or something along those lines) . f) The maximum angular velocity of the mass g) The maximum angular accleration of the mass h) The magnitude of the angular momentum of the mass at 3 seconds i) The magnitude of the torque acting on the mass at 3 seconds Problem 4: A wave has a wavenumber of 1 m-1, and an angular frequency of 2 radians per second, travels in the +x direction and has a maximum transverse amplitude of 0.1 m. At t=0, and x =0 the y position is equal to 0.0 m (y(0,0) = 0.0 m). a) Calculate the wavelength of the wave b) Calculate the period of oscillations for the wave c) Calculate the wave speed along the x axis d) Calculate the magnitude and direction of the transverse position of the wave at x=0.5 m and t = 8s e) Calculate the magnitude and direction of the transverse velocity of the wave at x=0.5 m and t = 8s f) Calculate the magnitude and direction of the transverse acceleration of the wave at x=0.5 m and t = 8s Problem 5-6: Chapter 16 Problem 10, 22 Additional Suggested Problems with Solutions Provided: Chapter 16 Problems 5, 9, 15, 45

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Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!

## Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!

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EEGR 221 MATLAB Project 1 Basic Signals Fall 2015 Due date: 10/5/15 1. (a) Plot ?1(?) = ?(?+1)−?(?−5) where -7 < t < 7 seconds. Use millisecond units. (b) Plot ? = 5 ??? (??)[ ?(?+1)−?(?−5)] 2. (a) Plot x2(t) exactly as shown in this figure. Include the same titles and labels for the signal. Hint: Find the amplitude equations as function of time and insert those to your MATLAB script to create and plot this signal. (b) Decompose x2(t) into its even and odd components and plot x2e(t) and x2o(t). (c) Plot x2e(t) + x2o(t) and verify that x2e(t) + x2o(t) = x2(t). How to report the results?  For each plot you must label x and y axis and have a title for the plot. Following commands could be used. heaviside, plot, axis, ylabel, ylabel, title, fliplr, etc … At the command prompt of MATLAB you can type >> help [command name] to get help with any command.  Plot all of the signal for t between -7 and 7 seconds.  Save your commands in an m-file with your name in the name field. (e.g. John_Scott.m) and append the code to the end of your report.  Your report must be organized and your solution for each question mu st be clearly marked by the number of the question. Example 2.a or 2.b, … In each part the problem should be clearly identified. Type the problem statement in each section. Show the plots of input and output signals. Draw conclusions based on your plots and in problem 3 discuss why the property is not satisfied based on your plots.  Turn in a hard copy of your report in class. This report must include a cover page with the name of both student partners.