Question

Find the inverse Laplace transform, f(t), of the function:

F(s) = 7/s^2 + 5s + 24

Answer 1

`y(t)=(14)/(√(71))e^{-(5)/(2)t}sin(√(71))/(2)t`

Explanation:

We are given that a function

F(s)=
`(7)/(s^2+5s+24)`

We have to find the inverse transform of the function

F(s)=
`(7)/(s^2+2\cdot (5)/(2)s+(25)/(4)-(25)/(4)+24)`

F(s)=
`(7)/((s+(5)/(2))^2+((√(71))/(2))^2)`

We know that laplace transform of sinhat

L(sinat)=
`(a)/(s^2+a^2)`

L
`(e^(at)sinbt)=(b)/((s-a)^2+b^2)`

Using this formula we get

`y(t)=(7)/((√(71))/(2))* e^{-(5)/(2)t}sin(√(71))/(2)t`

`y(t)=(14)/(√(71))e^{-(5)/(2)t}sin(√(71))/(2)t`