Question

Find the inverse Laplace transform, f(t), of the function: F(s) = 7/s^2 + 5s + 24

Answer 1

Answer:

$y(t)=\frac{14}{\sqrt{71}}e^{-\frac{5}{2}t}sin\frac{\sqrt{71}}{2}t$

Step-by-step explanation:

We are given that a function

F(s)=$\frac{7}{s^2+5s+24}$

We have to find the inverse transform of the function

F(s)=$\frac{7}{s^2+2\cdot \frac{5}{2}s+\frac{25}{4}-\frac{25}{4}+24}$

F(s)=$\frac{7}{(s+\frac{5}{2})^2+(\frac{\sqrt{71}}{2})^2}$

We know that laplace transform of sinhat

L(sinat)=$\frac{a}{s^2+a^2}$

L$(e^{at}sinbt)=\frac{b}{(s-a)^2+b^2}$

Using this formula we get

$y(t)=\frac{7}{\frac{\sqrt{71}}{2}}\times e^{-\frac{5}{2}t}sin\frac{\sqrt{71}}{2}t$

$y(t)=\frac{14}{\sqrt{71}}e^{-\frac{5}{2}t}sin\frac{\sqrt{71}}{2}t$