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1. Describe the graph of displacement versus time created on the preceding page: 2. Write an equation for x(t) in terms of o:

1. Describe the graph of displacement versus time created on the preceding page: 2. Write an equation for x(t) in terms of o:

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Please help with the questions on the second page. I have done the first page. Thank you!
9-7 Simple Harmonic Motion versus Uniform Circular Motion Questions: Simple harmonic motion is equivalent to the projection of uniform circular motion along the x axis. Assume an object moves in a 1.0 m-radius circle with a constant angular velocity of o = A/4 radians per second. How long will it take to complete one cycle? 1. Describe the graph of displacement versus time created on the preceding page: UCM SHM 2. Write an equation for x(t) in terms of o +Xo- 3. Assume instead that the obiect moves in a 2.0 m-radius circle with a constant angular velocity of o =1/2 radians per second. a) How long will it take to complete one cycle? b) Make a rough sketch of the x coordinate of the object as a function of time. 20 m X - Xo - 0m 1- t (s) 3- 6. -7 -8 -2.0m Record the object's angular displacement, 0, at each time, t, listed below. Mark its location on the circle and on the x axis below. Then calculate the x coordinate of the object and plot t as a function of time. (Hint: Use the sine function) c) Write an equation for x(t) in terms of o : t (s) 1 2 3 4 6 7 8 4) Assume the object graphed in question 3 is moving in simple harmonic motion. a) What is the frequency the motion, f? e (radians) 1/4 b) Write an equation for the relationship between angular velocity, w, and frequency, f. x (m) 10m c) Write an equation for the relationship between angular velocity, o, and period T. Х Om > t (s) 2. 4 7. 8 -1.0m ZEMO 56 hercee
Transcribed Image Text:9-7 Simple Harmonic Motion versus Uniform Circular Motion Questions: Simple harmonic motion is equivalent to the projection of uniform circular motion along the x axis. Assume an object moves in a 1.0 m-radius circle with a constant angular velocity of o = A/4 radians per second. How long will it take to complete one cycle? 1. Describe the graph of displacement versus time created on the preceding page: UCM SHM 2. Write an equation for x(t) in terms of o +Xo- 3. Assume instead that the obiect moves in a 2.0 m-radius circle with a constant angular velocity of o =1/2 radians per second. a) How long will it take to complete one cycle? b) Make a rough sketch of the x coordinate of the object as a function of time. 20 m X - Xo - 0m 1- t (s) 3- 6. -7 -8 -2.0m Record the object's angular displacement, 0, at each time, t, listed below. Mark its location on the circle and on the x axis below. Then calculate the x coordinate of the object and plot t as a function of time. (Hint: Use the sine function) c) Write an equation for x(t) in terms of o : t (s) 1 2 3 4 6 7 8 4) Assume the object graphed in question 3 is moving in simple harmonic motion. a) What is the frequency the motion, f? e (radians) 1/4 b) Write an equation for the relationship between angular velocity, w, and frequency, f. x (m) 10m c) Write an equation for the relationship between angular velocity, o, and period T. Х Om > t (s) 2. 4 7. 8 -1.0m ZEMO 56 hercee
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