Question

Find the L(sin^3 t).

(a) \(\frac{3}{4(s^2+1)}-\frac{1}{4(s^2+9)}\)

(b) \(\frac{3}{4(s^2+1)}-\frac{3}{4(s^2+9)}\)

(c) \(\frac{3}{4(s^2+1)}-\frac{9}{4(s^2+9)}\)

(d) \(\frac{3}{4(s^2-1)}-\frac{3}{4(s^2+9)}\)

This question was addressed to me during an interview.

My question comes from Table of General Properties of Laplace Transform in section Laplace Transform of Engineering Mathematics

Answer 1

The correct option is (b) \(\frac{3}{4(s^2+1)}-\frac{3}{4(s^2+9)}\)

To explain I would say: In the given question

= L(sin^3 t)

= \(L \left (\frac{3 sint}{4}\right )-L \left (\frac{1}{4} sin⁡(3t)\right )\)

= \(\frac{3}{4(s^2+1)}-\frac{3}{4(s^2+9)}\).