Answer:
[tex]y(t)=\frac{14}{\sqrt{71}}e^{-\frac{5}{2}t}sin\frac{\sqrt{71}}{2}t[/tex]
Step-by-step explanation:
We are given that a function
F(s)=[tex]\frac{7}{s^2+5s+24}[/tex]
We have to find the inverse transform of the function
F(s)=[tex]\frac{7}{s^2+2\cdot \frac{5}{2}s+\frac{25}{4}-\frac{25}{4}+24}[/tex]
F(s)=[tex]\frac{7}{(s+\frac{5}{2})^2+(\frac{\sqrt{71}}{2})^2}[/tex]
We know that laplace transform of sinhat
L(sinat)=[tex]\frac{a}{s^2+a^2}[/tex]
L[tex](e^{at}sinbt)=\frac{b}{(s-a)^2+b^2}[/tex]
Using this formula we get
[tex]y(t)=\frac{7}{\frac{\sqrt{71}}{2}}\times e^{-\frac{5}{2}t}sin\frac{\sqrt{71}}{2}t[/tex]
[tex]y(t)=\frac{14}{\sqrt{71}}e^{-\frac{5}{2}t}sin\frac{\sqrt{71}}{2}t[/tex]
