Question

Find the inverse laplace transform f(t)=l−1{f(s)} of f(s)=2s+8/s2+13s>0

Answer 1

we are given with

$f(s)=\frac{2s+8}{s^2+13}$

Re-write in the expanded form as below

$f(s)=2*\frac{s}{s^2+13}+8*\frac{1}{s^2+13}\\ \\ \text{Now take inverse Laplace Transform on both the sides we get}\\ \\ L^{-1}[f(s)]=L^{-1}[2*\frac{s}{s^2+13}+8*\frac{1}{s^2+13}]\\ \\ L^{-1}[f(s)]=2*L^{-1}\frac{s}{s^2+13}+8*L^{-1}\frac{1}{s^2+13}\\ \\ \text{From the Laplace inverse transform table we can re-write above equation as }\\ \\ f(t)=2cos\sqrt{13}t+ \frac{Sin\sqrt{13}t}{\sqrt{13}}$