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HW_14 - Physics 112 Homework#14 Fall 2006 Note This...

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Physics 112 Homework #14 Fall 2006 Note: This Homework includes material from Nov 15th to Dec 1 st and is longer that the other assignments. Read: Chapter 13 (all of it) For discussion: Chapter 13: Qs #Q13.1, Q13.4, Q13.5, Q13.6, Q13.7, Q13.12, Q13.13, Q13.14, (not turned in) Q13.15, Q13.16 Chapter 13: Es & Ps: #13.3, 13.9, 13.17, 13.23, 13.29, 13.31, 13.33, 13.41, 13.49, 13.80, 13.91, 13.95, 13.96 Due Friday, Dec 1 st at lecture: #13.16 [Inertia Balance] #13.19 [Oscillation Function] #13.27 [Energy in SHM] #13.45 [Pendulum on Another Planet] #13.63 [Block on Block + Spring] #13.54 [Driven Oscillations] 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 will be useful: sin 2 θ = (1 - cos2 θ )/2 and cos 2 θ = (1 + cos2 θ )/2.] (c) For two complete cycles
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