hw_9 - ME163 Mechanical Vibrations (Winter 2009) HW-9 Due...

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Unformatted text preview: ME163 Mechanical Vibrations (Winter 2009) HW-9 Due 3.12.09 1. Time Solution, three approaches. In this problem we will collect and compare three different approaches to obtaining the time solution to the equation: x + 2 n x + 2 n x = 1 f sin( f t ) where = 0 . 1, n = 10, and f = 1 / 5. The initial conditions are x (0) = x (0) = 0. (a) Calculate x(12), x(24), x(36) by assuming a solution x ( t ) = x sin ( f t- ) and using this assumed solution (and x and that you solve for) to obtain the three values. (b) Calculate x(12), x(24), x(36) using the convolution approach (use m = 1.0). The following integral may be useful. I = integraldisplay t e- a 2 sin( a 3 )sin( a 1 ( t- )) d = sin( a 1 t ) a 3 3- 2 a 1 a 2 cos( a 1 t ) a 3- a 2 1 sin( a 1 t ) a 3 + a 2 2 sin( a 1 t ) a 3 a 4 1 + 2 a 2 2 a 2 1- 2 a 2 3 a 2 1 + a 4 2 + a 4 3 + 2 a 2 2 a 2 3 + O ( ) where O ( ) is a messy term which is small in size and therefore you can neglect it....
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This note was uploaded on 03/23/2009 for the course ME 163 taught by Professor Mezic,i during the Winter '08 term at UCSB.

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hw_9 - ME163 Mechanical Vibrations (Winter 2009) HW-9 Due...

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