Question #343124

Find the Laplace transforms of the following function:

7. L{t^2 -3cos4t}


1
Expert's answer
2022-05-23T16:08:22-0400
L{f}(s)=0f(t)estdt{\cal L}\{f\}(s)=\int_0^{\infty}f(t)e^{-st}dtL{t23cos4t}(s)=0t2estdt30cos4testdt=2s33s16+s2=2s33s16+s2{\cal L}\{t^2-3\cos4t\}(s)\\ =\int_0^{\infty}t^2e^{-st}dt-3\int_0^{\infty}\cos4te^{-st}dt\\ =\frac{2}{s^3}-3*\frac{s}{16+s^2}\\ =\frac{2}{s^3}-\frac{3s}{16+s^2}

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