Question

Which of the following is not a term present in the Laplace Transform of e^2t sin^4 t.

(a) \(\frac{3}{8s}\)

(b) \(\frac{3}{8(s-2)}\)

(c) \(\frac{s}{8((s-2)^2+16)}\)

(d) \(\frac{s}{2((s-2)^2+4)}\)

The question was asked in an internship interview.

My question is based upon Table of General Properties of Laplace Transform in division Laplace Transform of Engineering Mathematics

Answer 1

Right answer is (a) \(\frac{3}{8s}\)

To explain: In the given question,

sin^4 t=\(\frac{1+cos^2(2t)-2cos⁡(2t)}{4}\)

L(sin^4 t)=\(L\left (\frac{1+cos^2 (2t)-2 cos⁡(2t)}{4}\right )\)

=\(\frac{3}{8s}-\frac{s}{2(s^2+4)}+\frac{s}{8(s^2+16)}\)

By First Shifting Property

L(e^2t sin^4 t)=\(\frac{3}{8(s-2)}-\frac{s}{2((s-2)^2+4)}+\frac{s}{8((s-2)^2+16)}\)