Question

The Laplace transform of the function e^-2tcos(3t) + 5e^-2tsin(3t) is ____________

(a) \(\frac{(s+2)-15}{(s+2)^2-9}\)

(b) \(\frac{(s+2)+15}{(s+2)^2-9}\)

(c) \(\frac{(s+2)+15}{(s+2)^2+9}\)

(d) \(\frac{(s+2)-15}{(s+2)^2+9}\)

I have been asked this question in an interview for internship.

My query is from Exponential Fourier Series and Fourier Transforms topic in chapter Fourier Series of Signals and Systems

Answer 1

Correct answer is (c) \(\frac{(s+2)+15}{(s+2)^2+9}\)

Easiest explanation: L {e^-2tcos(3t) + 5e^-2tsin(3t)}

= \(\frac{(s+2)}{(s+2)^2+9} + \frac{53}{(s+2)^2+9}\)

= \(\frac{(s+2)+15}{(s+2)^2+9}\).