Assignment_1_08 - TA's Name Section Your Name Physics 214...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
TA's Name:____________________ Section: ____ Your Name: _________________________________ Physics 214 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: AG Lecture Notes on Oscillations (from the website); Y&F, Vol. 1, Chapter 13 Assignment: Due in lecture on Tuesday, January 29. 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( ω t + φ) ? (b) In (a) you assumed that ω is real. But suppose that it has an imaginary component as well, i.e., ω = ω 0 + i ω 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 ω . Determine that ω . What are its real and imaginary parts?
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/31/2009 for the course PHYS 214 taught by Professor Thorne during the Spring '08 term at Cornell.

Page1 / 3

Assignment_1_08 - TA's Name Section Your Name Physics 214...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online