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General Physics(ppt) Ch 15 - Chapter 15 Oscillation Simple...

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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 dt x d dt dv a 2 2 2 ω - = - = = = m k = 2 ω Chapter 15 Oscillation ) 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.
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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 speedand position and the angular frequency of its motion, the phase angle and the amplitude of any particle moving in SHM can be determined. Chapter 15 Oscillation i i x v ω φ - = tan 2 2 2 2 2 2 2 sin cos ) ( A A A v x i i = + = + φ φ ω 2 2 ) ( ω i i v x A + =
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The block-spring system ma kx F s = - = m
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