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Unformatted text preview: Chapter 15 Oscillation Hooke’s law : F s = -kx Simple Harmonic Motion Mathematical representation of simple harmonic motion ma kx F s =- = m kx a- = x m kx d x d d dv a 2 2 2 ω- =- = = = m k = 2 ω Chapter 15 Oscillation m dt dt m ) cos( ) ( φ ω + = t A t x A: amplitude ω : angular frequency φ : phase angle ) ( φ ω + t : the phase of the motion T : period(= 2 π / ω ), the time it takes for particle to go through one full cycle. f : frequency(= ω /2 π ), the number of oscillations that the particle makes per unit time. Simple Harmonic Motion ) cos( ) ( φ ω + = t A t x φ cos A x i = Chapter 15 Oscillation ) sin( ) ( φ ω ω +- = = t A dt t dx v φ ω sin A v i- = ) cos( ) ( 2 φ ω ω +- = = t A dt t dv a φ ω cos 2 A a i- = x a 2 ω- = Simple Harmonic Motion φ cos A x i = φ ω sin A v i- = If we know the particle’s initial speed and position and the angular frequency of its motion, the phase angle and the amplitude of any particle moving in SHM can be determined....
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This note was uploaded on 12/27/2011 for the course LSCI 103 taught by Professor K.y.liao during the Fall '11 term at National Cheng Kung University.
- Fall '11