Find the inverse Laplace transform f(t) = L^(-1){F(s)} of the function F(s) = 8e^(-9s)/(s^2 + 64). Note: Use u(t) for the Heaviside function.
Added by Adam R.
Step 1
Recall that the Laplace transform of a time-shifted function \(f(t-a)u(t-a)\) is \(e^{-as}F(s)\), where \(F(s)\) is the Laplace transform of \(f(t)\) and \(u(t-a)\) is the Heaviside step function. This means we can separate the problem into finding the inverse Show more…
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