# 0 3 6 0 33 bm t bm the wave equation consider a wave

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Unformatted text preview: rnion operators. 0  )) () ' 2m This equation can be solved directly. m Find the velocity by taking the derivative with respect to time. ¢ . x> m The Damped Simple Harmonic Oscillator Generate the differential equation for a damped simple harmonic oscillator as done above.  2  ! 0, x, 0, 0 bdx dt 0, b x, 0, 0 0, Solve the equation. 0 3 6' 0 33 bm t bm The Wave Equation Consider a wave traveling along the x direction. The equation which governs its motion is given by ©  0, 0, f t v x ,0 The third term is the one dimensional wave equation. The forth term is the instantaneous power transmitted by the wave. ©  ¦ 0  ' 0, 0, f tv x, 0 )©  ¦ ) d2 dx2 d2 dt2 v2 2 d2 f t v x dt dx v  ¦ )) () ¤ d d , , 0, 0 v dt dx 2 ©¦  x >C 1 e 2m C2e 5 35 4 k m b2 m2 4 k m b2 m2 )) () ) & %&& & 0 )) () ) 5  3 4' & %&& &  0, kx , 0, 0 m ) ) d2 x dt2 0 t 3 ¤ ) () ¢& & ¤ d ,0 dt d ,0 dt ¡ 2 ©¦ k C 1 Cos kt m ©¦  x > C 2 Cos kt  ! 0, x, 0, 0 0, C 1 Sin kt m k C 2 Sin m ©¦ ¤ %&& d ,0 dt k x, 0, 0 m 0, kx , 0, 0 m kt m k x, 0, 0...
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## This note was uploaded on 09/30/2010 for the course MAE 123 taught by Professor 123 during the Spring '10 term at École Normale Supérieure.

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