Question

Given F(s) = \(\frac{3s+5}{s^2+7}\). The value of L^-1{F(s)} is _______________

(a) \(3 \,cos (\sqrt{7} t) + \frac{5}{\sqrt{7}} \,sin (\sqrt{7} \,t)\)

(b) \(3 \,cos (\sqrt{7} t)- \frac{5}{\sqrt{7}} sin (\sqrt{7} \,t)\)

(c) \(3 \,cos (\sqrt{7} t) \)

(d) \(\frac{5}{\sqrt{7}} \,sin (\sqrt{7} t)\)

The question was asked during an interview.

My query is from Common Laplace Transforms topic in division Laplace Transform and System Design of Signals and Systems

Answer 1

Correct choice is (a) \(3 \,cos (\sqrt{7} t) + \frac{5}{\sqrt{7}} \,sin (\sqrt{7} \,t)\)

To elaborate: Let, f (t) = L^-1 {F(s)}

= L^-1 \(\Big\{\frac{3s}{s^2+7} +  \frac{5}{s^2+7}\Big\}\)

= L^-1 \(\Big\{3 \frac{s}{s^2+\sqrt{7}^2} +  \frac{5}{\sqrt{7}}  \frac{\sqrt{7}}{s^2+\sqrt{7}^2}\Big\}\)

= \(3 \,cos (\sqrt{7} t) + \frac{5}{\sqrt{7}} \,sin (\sqrt{7} \,t)\).