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Phys 2214 Assignment 1 2011

Phys 2214 Assignment 1 2011 - TA's Name Section Your Name...

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TA's Name:____________________ Section: ____ Your Name: _________________________________ Physics 214, Spring 2008 1 Cornell University Physics 2214 Assignment 1 Concepts: complex numbers force law for SHM complex exponentials damped oscillations oscillations driven oscillations and resonance restoring forces decay time and resonance width simple harmonic motion oscillator equations Reading: Lecture Notes 1 & 2; Y&F, Vol. 1, Chapter 13 Assignment: Due at the beginning of your second recitation section meeting next week; either Wednesday, 8/31, or Thursday, 9/1. Please turn in this sheet stapled to the top of your work. A. Math Warm-Up Problems 1. (a) What are the real and imaginary parts of the function z(t) = r e i( t +  (b) In (a) you assumed that is real. But suppose that it has an imaginary component as well, i.e., = 0 + i 1 . What is the real part of z(t) in this case? (c) From your answer to (a), we can represent a real sinusoidal oscillation using the real part of a complex exponential, x(t) = Re [z]. Evaluate (i) dz/dt; (iii) dx/dt = d/dt { Re[z] }; and (ii) Re {dz/dt}. (d) Consider a second order differential equation of the form a d 2 x/dt 2 + b dx/dt + cx = 0 where a, b and c are constants. Show that x(t) = Re { [z(t)] }, where z(t) is as in (a), is a solution to this equation for a particular value of . Determine that . What are its real and imaginary parts?
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