example_IV_3_01_02

example_IV_3_01_02 - í ï î ï ü ý ï þ ï = -f mw n...

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Examples IV.3.1 and IV.3.2 Find the response x(t) of the system shown below with initial conditions of for: (a) (b) f t ( ) = f 0 t Compare the solution with that found by other means. x k m f(t) SOLUTION f t ( ) = f 0 x t ( ) = 1 mw n sin w n t - t ( ) f t ( ) 0 t ò dt = f 0 mw n sin w n t - t ( ) 0 t ò dt Let z = t - t Þ dz = - dt Þ t = 0 ® z = t Þ t = t ® z = 0 Therefore, x t ( ) = - f 0 mw n sin w n z t 0 ò dz = f 0 mw n 1 w n cos w n z [ ] z = t z =0 = f 0 mw n 2 1- cos w n t [ ]
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f t ( ) = f 0 t x t ( ) = 1 mw n sin w n t - t ( ) f t ( ) 0 t ò dt = f 0 mw n t sin w n t - t ( ) 0 t ò dt Let z = t - t Þ dz = - dt Þ t = 0 ® z = t Þ t = t ® z = 0 Therefore, x t ( ) = - f 0 mw n t - z ( ) sin w n z t 0 ò dz = - f 0 mw n t sin w n z t 0 ò dz - z sin w n z t 0 ò dz ì í ï î ï ü ý ï þ ï = - f 0 mw n t sin w n z t 0 ò dz - - z w n cos w n z é ë ê ù û ú t 0 - 1 w n cos w n z t 0 ò dz ì
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Unformatted text preview: í ï î ï ü ý ï þ ï = -f mw n t-1 w n cos w n z é ë ê ù û ú t--z w n cos w n z é ë ê ù û ú t-1 w n 1 w n sin w n z é ë ê ù û ú t ì í ï î ï ü ý ï þ ï = -f mw n-t w n 1- cos w n t ( )-t w n cos w n t + 1 w n 2 sin w n t ì í î ü ý þ = f mw n t w n-1 w n 2 sin w n t ì í î ü ý þ...
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This document was uploaded on 12/23/2011.

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example_IV_3_01_02 - í ï î ï ü ý ï þ ï = -f mw n...

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