Question

Use the convolution theorem to find the inverse Laplace transform of the given function. 4 s' (s2 + 4) **** 14.30-0 $(2+4)

Answer 1

Convolution theorem:

$L^{-1}[f(s).g(s)]=\int^{t}_{0}f(u).g(t-u)du$

Split the given function into two terms and apply inverse laplace transform.

$L^{-1}[\frac{1}{s^2+b^2}]=\frac{sinbt}{b}$

$L^{-1}[\frac{1}{s^n}]=\frac{t^{n-1}}{(n-1)!}$

After that apply in the formula, put t=u in f(t) function and put t=t-u in g(t) function.

Now do integration, apply limits, get final equation.

Formula used:

$Sin^2x+cos^2x=1$

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