Question

The Laplace transform of the function sin (4t) cos (2t) is ____________

(a) \(\frac{2}{s^2+16}\)

(b) \(\frac{2}{s^2-16}\)

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

(d) \(\frac{s^2-16}{2}\)

The question was posed to me in examination.

I need to ask this question from Common Laplace Transforms in section Laplace Transform and System Design of Signals and Systems

Answer 1

Right answer is (a) \(\frac{2}{s^2+16}\)

Explanation: L (\(\frac{1}{2}\) sin (4t))

= \(\frac{1}{2}\) L (sin (4t))

= \(\frac{1}{2} \frac{4}{s^2+16}\)

= \(\frac{2}{s^2+16}\).