Question

The Laplace transform of the function cosh^2(t) is ____________

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

(b) \(\frac{s^2-2}{s(s^2-4)}\)

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

(d) \(\frac{s^2+2}{s(s^2-4)}\)

I got this question during an interview.

I'm obligated to ask this question of Trigonometric Fourier Series in division Fourier Series of Signals and Systems

Answer 1

The correct choice is (b) \(\frac{s^2-2}{s(s^2-4)}\)

The explanation is: L ((\(\frac{1}{2}\)(e^t – e^-t))^2)

= L \(\left(\frac{e^2t}{4} + \frac{1}{2} + \frac{e^{-2t}}{4}\right)\)

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

= \(\frac{s^2-2}{s(s^2-4)}\).