ClassHarm

ClassHarm - 2 x(t) = A sin( (k/m) 1 / 2 t) x(t) = A sin 2...

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Classical Harmonic Oscillator Simple Harmonic Motion: Hooke's Law F = – kx x(t) = fcn(t) i.e. x is a function of time F = ma m x = 0 -A A m d 2 x(t) dt 2 = -k x(t) guess a solution: x(t) = A sin ct LHS: dx(t) dt = A (cos ct) c d 2 x(t) dt 2 = – c 2 A sin ct m d 2 x(t) dt 2 = –m c 2 A sin ct RHS: –kx(t) = –kA sin ct LHS=RHS – m c 2 A sin ct = –kA sin ct m c 2 = k c = (k/m) 1 /
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Unformatted text preview: 2 x(t) = A sin( (k/m) 1 / 2 t) x(t) = A sin 2 πν t ν = 1 2 π √ f8e5 k m Potential: ( ∂ V ∂ x ) = -F V = – ∫ Fdx V = ∫ kx dx = 1 2 kx 2 Total Energy : E = E K + V = 1 2 mv 2 + 1 2 kx 2 = ? when x(t) = A E K = 0 then E = 1 2 kA 2 For diatomic molecules replace m by μ = m 1 m 2 m 1 + m 2...
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This document was uploaded on 02/22/2012.

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