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Assignment_2_08

# Assignment_2_08 - TA's Name Section Your Name Physics 214...

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TA's Name:____________________ Section: ____ Your Name: _________________________________ Physics 214 Assignment 2 Concepts: damped oscillations traveling waves driven oscillatons and resonance wavelength, frequency damping regimes power in driven oscillations Reading: AG Lecture Notes on Mechanical Waves (from website); Y&F, Vol. 1, Chapter 15 Assignment: Due in lecture on Tuesday, February 5. Please turn in this sheet stapled to the top of your work. Physics Problems: 1. Damped oscillators. In our consideration of damped and driven oscillations with a damping force F = bv, we've focused so far on the case of light damping, This corresponds to ω 0 τ /2 >>1 where ω 0 2 = k/m and τ = 2m/b, so that there are many free oscillations in one decay time. Let's explore the more general case. (a) Free oscillations. Using the complex representation z(t) = Ae α t in the equation of motion, obtain an equation for α . Determine the solutions to this equation for (i) ω 0 τ >1 (underdamped), (ii) ω 0 τ =1 (critically damped) and (iii) ω 0 τ <1 (overdamped), where ω 0 2 = k/m and τ =2m/b. In each case, write down the solution for x(t) implied by the solutions for α , in terms of ω 0 and τ . (Note: there may be more than one solution for a given ω 0 and τ , so x(t) will in general be a sum of the solutions.

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Assignment_2_08 - TA's Name Section Your Name Physics 214...

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