# ps02 - Physics 2214 Problem Set#2(Due 11:15 am Thursday 1 A...

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Page 1 of 2 Physics 2214 Problem Set #2 (Due 11:15 am, Thursday 9/11/08) 1. A driven oscillator with mass m , spring constant k , and damping coefficient b is driven by a force F 0 cos ω t . The resulting steady-state oscillations are described by { } () Re it x tA e ω = where 0 0 22 0 / () ( 2 / ) i Fm AA e i φ ωω τ == −+ , 0 / km , and τ 2 m / b . (a) Find the driving frequency at which the amplitude A is maximum. Do not assume light damping. (b) Show that for light damping ( τω 0 ب 1), the maximum amplitude occurs at approximately ω = ω 0 . (c) Plot graphs of A and as functions of ω / ω 0 for the case 0 = 8. Use a logarithmic scale for the ω / ω 0 axis. Approximately what is the maximum amplitude? 2. (a) Show that { } { } { } Re Re Re A BA B = if and only if at least one of A and B is a real number. (b) Use Euler’s identity to prove * 0 1 cos ( ) 2 At A e A e ωφ += + where 0 i e = and 0 * i e = . ( * A is called the complex conjugate of A .) 3. The instantaneous power delivered to a driven oscillator by the driving force is 0 cos xx dx Pt F F t dt + v

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ps02 - Physics 2214 Problem Set#2(Due 11:15 am Thursday 1 A...

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