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ps03 - Physics 214 Problem Set#3(Due 11:15 am Thursday 1 A...

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Page 1 of 3 Physics 214 Problem Set #3 (Due 11:15 am, Thursday 9/18/08) 1. A transverse wave on an ideal string (no forces other than tension) is described by y ( x,t ) = A e i ( kx + ω t ) where A = (–0.35 mm) – i (0.20 mm), ω = 2510 rad/s, and k = 50.2 rad/m. The mass per unit length is 0.025 kg/m. (Taking the real part to obtain y ( x,t ) is understood.) (a) Sketch a snapshot (a graph of y vs. x ) of the string at t = 0, with numerical values on the axes. Show at least two complete cycles. Identify one point on your graph for each of the following conditions: maximum particle velocity upward, zero particle velocity, maximum particle acceleration downward, and zero particle acceleration. Give the numerical values of the maximum velocity and acceleration. (b) What are the wave speed and direction of propagation? (c) What is the maximum vertical force on a segment of string due to the neighboring segment on the left (force exerted on one side only , not the net force)?
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