Phys 2214 Assignment 2 2011 - TA's...

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Unformatted text preview: TA's Name:____________________ Section: ____ Your Name: _________________________________ Physics 214, Spring 2009 1 Cornell University Physics 214 Assignment 2 Concepts: damped oscillations driven oscillatons and resonance damping regimes power in driven oscillations Reading: Lecture Notes for lectures 2 and 3 (on BB); Y&F, Vol. 1, Chapter 13 Assignment: Due in section, week of Sept. 5, 2011. 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 t x t Ae ( ) Re{ } 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 A be so that the oscillation frequency deviates from by (i) 0.1%? (ii) 1%? (iii) 10%? (c) How does (i) the time required to relax from an initial displacement and (ii) the amount of oscillation that occurs during the relaxation compare for the underdamped, overdamped and critically damped cases? 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 to an oscillating force F(t) at frequency D : Physics 214, Spring 2009...
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Phys 2214 Assignment 2 2011 - TA's...

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