Use a table of Laplace transforms to find the Inverse Laplace transform

inverse-transform

#1

Use a table of Laplace transforms to find the Inverse Laplace transform of
image

Answer:

image

From table of Laplace Transform

\pounds^{-1}\left ( \frac{s}{s^2+a^2} \right )=cos(at) \ and \ \pounds^{-1}\left( \frac{a}{s^2+a^2} \right )=sin(at)

Therefore,

f(t)=5\pounds^{-1}\left ( \frac{s}{s^2+2^2} \right )+2\pounds^{-1}\left ( \frac{2}{s^2+2^2} \right )

f(t)=5cos(2t)+2sin(2t)