2hw2 - Physics 315 Oscillations and Waves Homework 2 Due in...

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Physics 315: Oscillations and Waves Homework 2: Due in class on Wednesday, Sep. 16th 1. Demonstrate that in the limit ν 2 ω 0 the solution to the damped har- monic oscillator equation becomes x ( t ) = ( x 0 + [ v 0 + ( ν/ 2) x 0 ] t ) e ν t/ 2 , where x 0 = x (0) and v 0 = ˙ x (0). 2. What are the resonant angular frequency and quality factor of the circuit pictured below? What is the average power absorbed at resonance? . I 0 cos( ω t ) L R C 3. The power input a P A required to maintain a constant amplitude oscillation in a driven damped harmonic oscillator can be calculated by recognizing that this power is minus the average rate that work is done by the damping force, m ν ˙ x . (a) Using x = x 0 cos ( ω t ϕ ), show that the average rate that the damping force does work is m ν ω 2 x 2 0 / 2. (b) Substitute the value of x 0 at an arbitrary driving frequency and, hence, obtain an expression for a P A . (c) Demonstrate that this expression yields Equation (3.56) of the lecture notes in the limit that the driving frequency is close to the resonant frequency.
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This note was uploaded on 11/02/2010 for the course PHY 315 taught by Professor Staff during the Spring '08 term at University of Texas.

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2hw2 - Physics 315 Oscillations and Waves Homework 2 Due in...

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