example_IV_3_01_02

# example_IV_3_01_02 - 1 n 1 n sin n z t = f m n t n 1 cos 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 x 0 ( ) = ˙ x 0 ( ) = 0 for: (a) f t ( ) = f 0 (b) f t ( ) = f 0 t Compare the solution with that found by other means. SOLUTION f t ( ) = f 0 x t ( ) = 1 m ω n sin n t τ ( ) f ( ) 0 t d = f 0 m n sin n t ( ) 0 t d Let z = t dz = d = 0 z = t = t z = 0 Therefore, x t ( ) = f 0 m n sin n z t 0 dz = f 0 m n 1 n cos n z [ ] z = t z = 0 = f 0 m n 2 1 cos n t [ ]

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f t ( ) = f 0 t x t ( ) = 1 m ω n sin n t τ ( ) f ( ) 0 t d = f 0 m n sin n t ( ) 0 t d Let z = t dz = d = 0 z = t = t z = 0 Therefore, x t ( ) = f 0 m n t z ( ) sin n z t 0 dz = f 0 m n t sin n z t 0 dz z sin n z t 0 dz = f 0 m n t sin n z t 0 dz − − z n cos n z t 0 1 n cos n z t 0 dz = f 0 m n t 1 n cos n z t 0 − − z n cos n z t 0
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Unformatted text preview: 1 n 1 n sin n z t = f m n t n 1 cos n t ( ) t n cos n t + 1 n 2 sin n t = f m n t n 1 n 2 sin n t...
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## This document was uploaded on 12/23/2011.

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example_IV_3_01_02 - 1 n 1 n sin n z t = f m n t n 1 cos n...

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