Question

The Laplace transform of the signal t u(t) * cos 2πt u(t) is _____________

(a) \(\frac{1}{s(s^2+4π^2)}\)

(b) \(\frac{2π}{s^2 (s^2+4π^2)}\)

(c) \(\frac{1}{s^2 (s^2+4π^2)}\)

(d) \(\frac{s^3}{(s^2+4π^2)}\)

This question was posed to me in an interview for internship.

Enquiry is from Common Laplace Transforms topic in section Laplace Transform and System Design of Signals and Systems

Answer 1

The correct answer is (a) \(\frac{1}{s(s^2+4π^2)}\)

The best explanation: p (t) = t u (t)

Laplace transform of p (t), p (s) = \(\frac{1}{s^2}\)

Again, q (t) = cos 2πt u (t)

Laplace transform of q (t), q (s) = \(\frac{s}{(s^2+4π^2)}\)

Again, x (t) = p (t) * q (t)

Laplace transform of x (t), x (s) = \(\frac{1}{s(s^2+4π^2)}\).