HW10 - PHYS 3202 Classical Mechanics II - Homework #10 Due...

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PHYS 3202 Classical Mechanics II - Homework #10 Due at 12:05pm, Monday April 25, 2011 in the class Please show intermediate steps of your calculations. If necessary, you may draw diagram(s). Problem 1 (10 points): Determine the motion of the continuous string with two fixed end points at x = 0 and x = L , and with initial conditions q ( x, 0) = A sin 2 ( πx/L ) and ˙ q ( x, 0) = 0. Then give a simple expression for q ( x,t ) at time t = L/v , where v = p τ/ρ , τ is the tension of the string, and ρ is its linear mass density. Hint: the general formula at arbitrary t may be an infinite series, but at t = L/v there is a simpler expression. Problem 2 (10 points): Find the total energy E of the string in Problem 1, as well as the energy E 1 of the lowest normal mode. Calculate the percentage E 1 /E . Problem 3 (10 points): If the wave equation 2 q ∂t 2 = v 2 2 q ∂x 2 , - ∞ < x < is solved with initial conditions q ( x, 0) = 0 and ˙ q ( x, 0) = f ( x ), where f ( x ) is a
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This note was uploaded on 01/22/2012 for the course PHYS 3202 taught by Professor Tan during the Spring '11 term at Georgia Institute of Technology.

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HW10 - PHYS 3202 Classical Mechanics II - Homework #10 Due...

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