Laplace Transform of t ^{2}sin(2t)? ...?
1 answer:
By laplace transform definition of { t^n * f(t) } <span>(-1)^n * ( d^n/ds^n ) F(s) </span> <span>t^2*sin(2t) <==== let's apply it </span> <span>(-1)^2 * ( d^2/ds^2 ) ( 2 / (s^2 + 2^2) ) </span> <span>1 * ( d^2/ds^2 ) ( 2 / (s^2 + 4) ) <===== let's find the first and second derivative : </span> <span>( (s^2 + 2^2) * 0 - 2 * (2s) / (s^2 + 4)^2 ) </span> <span>( - 4s) / (s^2 + 4)^2 ) <==== let's find the second derivative </span> <span>( (s^2 + 4)^2 * -4 - - 4s * 2 * (s^2 + 4) * 2s ) / (s^2 + 4)^4 ) </span> <span>( -4(s^2 + 4)^2 + 16s^2 * (s^2 + 4) ) / (s^2 + 4)^4 ) </span> <span>( -4(s^2 + 4) + 16s^2 ) / (s^2 + 4)^3 ) </span> <span>( -4s^2 - 16 + 16s^2 ) / (s^2 + 4)^3 ) </span> <span>( 12s^2 - 16 ) / (s^2 + 4)^3 ) I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead! </span>
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