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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online