Question

The Laplace transform of F(t) = sin(2t)cos(2t) is ______________

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

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

(c) \(\frac{2}{s^3}\)

(d) \(\frac{1}{2s} + \frac{s}{2(s^2+36)}\)

Answer 1

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

Explanation: Using the Trigonometric Identity,

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

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