OscillationsEssentials

# OscillationsEssentials - Oscillations:theEssentials 3/22/07...

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Oscillations: the Essentials 3/22/07 Complex Numbers Be familiar with the complex plane: i x iy re q + = , definitions: mod , phase of . z z r z = = = To multiply complex numbers, multiply the mods, add the phases. Know the all­important formula: cos sin , i e i q = + and be able to interpret it as a point on the unit circle . Some useful small x approximations: ( ) ( ) 1 1 2 1 , ln 1 , 1 1 , 1 1 x e x x x x x x x - @ + + @ + @ + + @ - and for small angles 2 1 2 sin tan , cos 1 . @ @ @ - Undamped Simple Harmonic Oscillator: Be able to solve the equation 2 2 , or , d x F ma m kx dt = = - and write down the velocity and kinetic energy at any time. Be able to sketch a graph of the potential energy as a function of position, both for a horizontal and a vertical spring. Be able to derive the angular frequency and the period. Know how to find the dependence of the period on k , m using dimensional arguments. A Heavily Damped Oscillator: You should know the equation of motion 2 2 d x dx m kx b dt dt = - - and that a solution is 0 .

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## This note was uploaded on 12/07/2011 for the course PHYSICS 152 taught by Professor Michaelfowler during the Fall '07 term at UVA.

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OscillationsEssentials - Oscillations:theEssentials 3/22/07...

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