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Homework6 - Physics 321 Spring 2006 Homework#6 Due at...

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Physics 321 – Spring 2006 Homework #6, Due at beginning of class Wednesday Mar 1. 1. [4 pts] A hook is at height y above the floor, where y is constant for all negative times: y = y 0 for t < 0. For positive times, y oscillates: y = y 0 + A sin ωt for t > 0. A mass M hangs from an ideal spring attached to this hook. The mass is at height x above the floor. The mass hangs motionless at x = x 0 = y 0 - Mg/k for t < 0, where k is the spring constant. Let ω 0 = q k/M as usual. (a) Find the motion x ( t ) of the mass for t > 0 if ω = 2 ω 0 . (b) Find the motion x ( t ) of the mass for t > 0 if ω = ω 0 . (You can do this by first finding x ( t ) for arbitrary ω and then carefully taking the limit ω ω 0 ; or if you’re chicken, you can set ω ω 0 in the equation of motion and solve it.) 2. [4 pts] A driven harmonic oscillator obeys the equation ¨ x + x = t ( A - t ) for 0 < t < A . Given the initial conditions x = ˙ x = 0 at t = 0, find the subsequent motion x ( t ) during the time interval 0 < t < A . 3. [4 pts] Marion & Thornton, problem 3-20 (Same in 4th edition). Do this problem by hand (i.e., using algebra, not using a computer). You need to find the two
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