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hw13s06 - Physics 112 Read Homework#13 Spring 2006 Chapter...

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Physics 112 Homework #13 Spring 2006 Read: Chapter 13 (intro., sections 13.1 thru 13.4) For study: Chap. 13: Qs #Q13.1, Q13.4, Q13.5, Q13.6, Q13.7 (not turned in) Chap. 13: Es & Ps: #13.3, 13.9, 13.17, 13.23, 13.29, 13.31, 13.33, 13.80, 13.95, 13.96 Due Friday, April 29 at lecture: 13.2 [Oscillator] #13.4 [Graph] #13.27 [Energy in SHM] #13.71 [SHM of Butcher's Scale] 1. [SHM Functions & Graphs] The position as a function of time t for a block of mass m oscillating on a horizontal ideal spring of spring constant k is x(t) = A cos( ω t). (a) Write the oscillator's velocity v(t) and acceleration a(t) in the form C cos( ω t + φ ), with C > 0, and find the constants C and φ for each function. (b) Write the oscillator's kinetic energy K(t) and elastic potential energy U(t) as functions of time t that are linear in sine or cosine of t. [HINT: The following trig identities may be useful: sin 2 θ = (1 - cos2 θ )/2 and cos 2 θ = (1 + cos2 θ )/2.] (c) For two complete cycles of this oscillation, draw graphs showing the oscillator's position x(t), velocity v(t), acceleration a(t), net force F(t), potential energy U(t), kinetic energy K(t), and total energy U(t) + K(t) as functions of time t. Please align all your graphs above one another on the same page with their time axes synchronized. (d) Make a plot of v vs. x. That is for each time, t, the block has some position x(t) and some velocity v(t). Draw the curve in the x-v plane which corresponds to the motion during one period.
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