Physics_1112__Spring_2009__Co_op_14__Oscillations - Name...

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Name:_____________________ Partners: __________________________ -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 0 0.5 1 1.5 2 Time (s) Cooperative Problems Week 14: Oscillations 1. Your task is to design a damped harmonic oscillator consisting of a mass of 0.050 kg on an ideal spring. The damping is supplied by a linear drag force f d = –bv, where v is the oscillator's velocity. The oscillator's free oscillations are to behave as shown in the graph. (a) What is the quality factor "Q" of this oscillator? [Hint: Q is π times the number of cycles for the amplitude to decrease to 1/e times its initial value.] (b) What are the values of A 0 ( > 0), τ , ω′ , and φ in the expression for the oscillator's position as a function of time t: x(t) = A 0 e –t/ τ cos( ω′ t + φ )? What is the mathematical relationship between Q, τ , and ω′ ? (c) What are the appropriate values for the spring constant k and drag force constant b? [Hint: τ = 2m/b; for light damping, ω′ / km .] Displacement (mm)
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(d) Now the oscillator is driven by a sinusoidal applied driving force at angular frequency ω . The oscillation amplitude as a function of ω
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Physics_1112__Spring_2009__Co_op_14__Oscillations - Name...

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