Laplace Transform of periodic function ( with Animation)

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  1. Digital Blackboard by Sachin P. Nagmote
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Consider an at rest second order system described by

y''+9y=9cos( 3t)
The response of this system will be

Oscillatory
A growing oscillation.
A decreasing oscillation.
None of the above.

knowledges
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Sir, how to find the Fourier transform of the same function???

Mikehydra
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Sir, does T denote the time period of first cycle or total time? Lets say I have 3 cycles of total time 3pi. so, my T will be 3pi or do i keep T=pi and multiply the laplace transform by 3 for 3 cycles? Thnks.

ace_krish