Assignment_2_09

Assignment_2_09 - TA's Name:_ Section: _ Your Name: _...

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TA's Name:____________________ Section: ____ Your Name: _________________________________ Physics 214, Spring 2009 1 Cornell University 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 3. Please turn in this sheet stapled to the top of your work. Physics Problems: 1. Free oscillations. (a) The online lecture notes give expressions for x(t) in the underdamped, overdamped and critically damped cases, in terms of and . Sketch the shape of the solution for x(t) in each of these cases, on same set of axes. In all cases, assume the initial conditions x(t=0) = A and v(t=0)=0. (Feel free to use a spreadsheet/plotting program.) (b) In the underdamped case , show that the imaginary part of - which gives the frequency of oscillations, has a magnitude What must 0 A be so that the oscillation frequency deviates from 0 by (i) 0.1%? (ii) 1%? (iii) 10%? (c) What is special about the critically damped case? For each of the following systems, would you like the response to be underdamped, overdamped, or critically damped? Explain briefly. (i) Auto suspension system; (ii) door bell; (iii) speaker cone; (iv) pogo stick; (v) cymbal; (vi) drum head; (vii) spring bathroom scale; (viii) bungee cord + person. 2. Driven oscillations. In lecture we derived the following expression for the complex amplitude of the response of a driven damped oscillator: (a) Determine expressions for the magnitude and phase of
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Physics 214, Spring 2009 2 Cornell University (b) Show (by taking the derivative and setting it to zero) that the maximum magnitude of occurs at a frequency where . (c) Determine this maximum magnitude , expressing it in terms of (the magnitude at low frequencies) and the quality factor Q only . (d) Suppose that you want to use a driven mechanical oscillator to detect tiny masses, as discussed in lecture. Assume that your oscillator is underdamped and has Q=10,000. What fractional change in mass m/m will cause the resonant frequency to shift by the width of the resonance? (Make reasonable approximations.) (e) If the noise in one's measuring system is sufficiently small to allow very accurate measurement of the resonance curve, it is possible to do much better than in ( d ). What fractional deviation in the oscillation amplitude from its peak value at resonance A/A max must you be able to resolve in order to detect a change in oscillator mass of one part in
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This note was uploaded on 04/04/2009 for the course PHYS 214 taught by Professor Thorne during the Spring '08 term at Cornell.

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Assignment_2_09 - TA's Name:_ Section: _ Your Name: _...

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