Midterm1solutions

Midterm1solutions - Physics 1C, Summer 2011 (Session 1)...

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Physics 1C, Summer 2011 (Session 1) Midterm 1 (50+5 points) Solutions Problem 1 (4+4+6 = 14 points) A particle is undergoing simple harmonic motion. Its velocity is given by the equation v(t) = (230 m/s)*sin[(1000s -1 )*t]. Give the answers to the following questions in SI units: a. What is the amplitude of the particle's motion? b. What is the period of the oscillatory motion? c. What is the first time t after t = 0 seconds that the particle will reach its equilibrium position? Solution a. The maximum speed is 230 m/s = ω A, where A is the amplitude and ω = (1000s -1 ) can be read off from the problem statement. This gives A = 0.23 meters. b. The period T = (2 π )/ ω = 6.3 ms. c. This is the value of t for which (1000s -1 )*t = ( π /2) radians: t = 1.57 ms. Problem 2 (4+4 = 8 points) Suppose you would like to create a pendulum with a 10 kg bob such that the period is exactly one second. a. What length of string should you use to create your pendulum? b. What length of string should you use if instead you use a 20 kg bob?
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Midterm1solutions - Physics 1C, Summer 2011 (Session 1)...

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