Essay list

## Essay list

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PlotCycloidArc(8.5) Math98 HW4 The cylcoid is the plane curve traced out by a point on a circle as the circle rolls without slipping on a straight line.1 In this exercise we will use MATLAB to create an animation of a circle rolling on a straight line, while a point on the circle traces the cycloid. a. Implement a MATLAB function of the form function PlotCycloidArc(ArcLength). This function takes in a positive number ArcLength and displays a snapshot of the cirle rolling (without slipping) on the x-axis while a point on the cirlce traces the cycloid. The circle is initially centered at (0,1) and has radius 1, and the initial tracing point is taken to be (0, 0). An example output is shown in the above ?gure. As in the ?gure, plot the cycloid arc black, the circle blue, and use a red dot for the tracing point. Hint: If the circle has rolled for a length of arc t = 0, the coordinates of the tracing point are (t-sin t, 1-cos t). b. Implement a MATLAB function of the form function CycloidMovie(NumHumps,NumIntervals). This function will output an animation of the circle rolling along a line while a point on the circle traces the cycloid. This function inputs two natural numbers NumHumps and NumIntervals representing the number of periods (or humps) of the cycloid and the number or frames per hump that will be used to make the animation, respectively. Use the getframe command to save frames outputted from PlotCycloidArc and the movie command to play them back together as a movie. Use the axis command to view the frames on the rectan- gle [0, 2pNumHumps] × [0, 5/2]. Also label the ticks 0, 2p, . . . , 2pNumHumps on the x axis with the strings 1See Wikipedia for more on the cycloid. 0, 2p, . . . , 2pNumHumps and do the same for 1, 2 on the y axis (see the ?gure above). Label the movie ’Cycloid Animation’. Submit MATLAB code for both parts a and b and a printout the ?gures obtained by the commands PlotCycloidArc(8.5), PlotCycloidArc(12), and CycloidMovie(3,10)

## PlotCycloidArc(8.5) Math98 HW4 The cylcoid is the plane curve traced out by a point on a circle as the circle rolls without slipping on a straight line.1 In this exercise we will use MATLAB to create an animation of a circle rolling on a straight line, while a point on the circle traces the cycloid. a. Implement a MATLAB function of the form function PlotCycloidArc(ArcLength). This function takes in a positive number ArcLength and displays a snapshot of the cirle rolling (without slipping) on the x-axis while a point on the cirlce traces the cycloid. The circle is initially centered at (0,1) and has radius 1, and the initial tracing point is taken to be (0, 0). An example output is shown in the above ?gure. As in the ?gure, plot the cycloid arc black, the circle blue, and use a red dot for the tracing point. Hint: If the circle has rolled for a length of arc t = 0, the coordinates of the tracing point are (t-sin t, 1-cos t). b. Implement a MATLAB function of the form function CycloidMovie(NumHumps,NumIntervals). This function will output an animation of the circle rolling along a line while a point on the circle traces the cycloid. This function inputs two natural numbers NumHumps and NumIntervals representing the number of periods (or humps) of the cycloid and the number or frames per hump that will be used to make the animation, respectively. Use the getframe command to save frames outputted from PlotCycloidArc and the movie command to play them back together as a movie. Use the axis command to view the frames on the rectan- gle [0, 2pNumHumps] × [0, 5/2]. Also label the ticks 0, 2p, . . . , 2pNumHumps on the x axis with the strings 1See Wikipedia for more on the cycloid. 0, 2p, . . . , 2pNumHumps and do the same for 1, 2 on the y axis (see the ?gure above). Label the movie ’Cycloid Animation’. Submit MATLAB code for both parts a and b and a printout the ?gures obtained by the commands PlotCycloidArc(8.5), PlotCycloidArc(12), and CycloidMovie(3,10)

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(2-3i)/(3+4i) in the form of a+ib

## (2-3i)/(3+4i) in the form of a+ib

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ELEC153 Circuit Theory II M2A1 Textbook Assignment: Problem Set A: Chapter 15 Instructions Save this document and place your answers into it so you can submit it to the appropriate homework dropbox. Handwritten solutions should be scanned and saved as a BMP, GIF, or JPG image, or scanned and pasted into this document. Questions 1. Find the impedance of this AC series circuit as seen from the two open-ended terminals. Show your answer in rectangular and polar form. The AC signal frequency is 1 KHz. 2. Repeat your analysis of Question 1 for a frequency of 200 Hz. 3. Consider the following AC series circuit: a. Find the total impedance across the voltage source in polar form. b. Find the source current, in polar form. Note: the source voltage is 20 volts rms at 0 degrees. c. Find the voltage across each component, in polar form. d. Find the real power supplied to the circuit, in Watts. ELEC153 Circuit Theory II M2A2 Textbook Assignment: Problem Set B: Chapter 15 Instructions Save this document and place your answers into it so you can submit it to the appropriate homework dropbox. Handwritten solutions should be scanned and saved as a BMP, GIF, or JPG image, or scanned and pasted into this document. Questions 1. Find the impedance of this AC parallel circuit between the two open-ended terminals, in rectangular and polar forms: 2. Consider the following AC parallel circuit: a. Find the total impedance across the voltage source in polar form. b. Find the source current, in polar form. Note: the source voltage is 12 volts rms at 0 degrees. c. Find the current through each component, in polar form. d. Find the real power supplied to the circuit, in Watts.

## ELEC153 Circuit Theory II M2A1 Textbook Assignment: Problem Set A: Chapter 15 Instructions Save this document and place your answers into it so you can submit it to the appropriate homework dropbox. Handwritten solutions should be scanned and saved as a BMP, GIF, or JPG image, or scanned and pasted into this document. Questions 1. Find the impedance of this AC series circuit as seen from the two open-ended terminals. Show your answer in rectangular and polar form. The AC signal frequency is 1 KHz. 2. Repeat your analysis of Question 1 for a frequency of 200 Hz. 3. Consider the following AC series circuit: a. Find the total impedance across the voltage source in polar form. b. Find the source current, in polar form. Note: the source voltage is 20 volts rms at 0 degrees. c. Find the voltage across each component, in polar form. d. Find the real power supplied to the circuit, in Watts. ELEC153 Circuit Theory II M2A2 Textbook Assignment: Problem Set B: Chapter 15 Instructions Save this document and place your answers into it so you can submit it to the appropriate homework dropbox. Handwritten solutions should be scanned and saved as a BMP, GIF, or JPG image, or scanned and pasted into this document. Questions 1. Find the impedance of this AC parallel circuit between the two open-ended terminals, in rectangular and polar forms: 2. Consider the following AC parallel circuit: a. Find the total impedance across the voltage source in polar form. b. Find the source current, in polar form. Note: the source voltage is 12 volts rms at 0 degrees. c. Find the current through each component, in polar form. d. Find the real power supplied to the circuit, in Watts.

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Chapter 6 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, March 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy PSS 6.1 Equilibrium Problems Learning Goal: To practice Problem-Solving Strategy 6.1 for equilibrium problems. A pair of students are lifting a heavy trunk on move-in day. Using two ropes tied to a small ring at the center of the top of the trunk, they pull the trunk straight up at a constant velocity . Each rope makes an angle with respect to the vertical. The gravitational force acting on the trunk has magnitude . Find the tension in each rope. PROBLEM-SOLVING STRATEGY 6.1 Equilibrium problems MODEL: Make simplifying assumptions. VISUALIZE: Establish a coordinate system, define symbols, and identify what the problem is asking you to find. This is the process of translating words into symbols. Identify all forces acting on the object, and show them on a free-body diagram. These elements form the pictorial representation of the problem. SOLVE: The mathematical representation is based on Newton’s first law: . The vector sum of the forces is found directly from the free-body diagram. v  FG T F  = = net i F  i 0