Question

The Laplace transform of f(t) = sin(2t) cos(2t) is ____________

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

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

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

(d) \(\frac{1}{2}\)

I had been asked this question in quiz.

I'm obligated to ask this question of Common Laplace Transforms topic in section Laplace Transform and System Design of Signals and Systems

Answer 1

Right choice is (b) \(\frac{1}{2}{\frac{4}{s^2+16}}\)

The explanation is: Using trigonometric identity,

We get, sin (2t) cos (2t) = \(\frac{1}{2}\) sin⁡(4t)

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

We know that, L {sin at} = \(\frac{a}{s^2+a^2}\)

∴L{\(\frac{1}{2}\) sin⁡(4t)} = \(\frac{1}{2}{\frac{4}{s^2+16}}\).