lec11-203-08-SHM

lec11-203-08-SHM - Spring: Simple Harmonic Motion Dynamics...

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-kx F = -kx ma = 0 x m k a = + 0 x ω a 2 = + m k ω = ma F = Hooks Law (Newton & Hook were bitter rivals) Newton says simple harmonic motion δ) ωt ( sin A x + = δ) ωt ( cos ω A v + = δ) ωt ( sin ω A a 2 + = Spring: Simple Harmonic Motion Dynamics f π 2 ω = T 1 f = angular freq. (rad./sec.) period (sec.) frequency (Hz = sec. -1 ) 11-1
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x= A x = 0 x= -A 2 2 kx 2 1 mv 2 1 E + = 2 kA 2 1 E = 2 kA 2 1 E = 2 max mv 2 1 E = cyclic transfer :: kinetic energy potential energy 2 max 2 mv 2 1 kA 2 1 = m k A v max = Energy 11-2
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A θ = ω t ) ωt ( sin A x = θ = ω t v v x = v cos( θ ) x a a = v 2 /A A ω v = a = ω 2 /A uniform circular motion- simple harmonic motion analogy 11-3
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If m= 1.0kg k= 100 N/m v max of 0.5m/s find A, T, f, x A, T, f, x max max , , a a max max sec rad 10 kg 1 m / N 100 m k = = = ω Hz 6 . 1 T 1 sec; 628 . 0 2 T = = = ω π = f rad x(t)=Asin(ωt)=Asin(10 t) sec 2 2 max max 1 1 mv = kx 2 2 Energy Con. 2
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This note was uploaded on 04/14/2008 for the course PHYSICS 203 taught by Professor Croft during the Spring '08 term at Rutgers.

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lec11-203-08-SHM - Spring: Simple Harmonic Motion Dynamics...

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