Question

Find the Laplace transform of the function f(t) = cos2t.

(a) (2s^2+4)/2s(s^2-4)

(b) (2s^2-4)/2s(s^2-4)

(c) (2s^2-4)/2s(s^2+4)

(d) (2s^2+4)/2s(s^2+4)

This question was posed to me in an international level competition.

This intriguing question originated from Operational Transforms topic in chapter Intoduction to the Laplace Transform of Network Theory

Answer 1

Right choice is (d) (2s^2+4)/2s(s^2+4)

The explanation: The Laplace transform of the function f(t) = cos2t is L (cos2t) = L((1+cos2t)/2) = L(1/2)+L(cos2t/2)  = 1/2[L(1)+L(cos2t)] = (2s^2+4)/2s(s^2+4).