Question

Find the L(t e^-2t sinh⁡(4t)).

(a) \(\frac{8s+16}{(s^2+2s-12)^2}\)

(b) \(\frac{2s+16}{(s^2+2s-12)^2}\)

(c) \(\frac{8s+16}{(s^2+21s-12)^2}\)

(d) \(\frac{8s+16}{(s^2+s-12)^2}\)

I have been asked this question by my school principal while I was bunking the class.

The query is from Table of General Properties of Laplace Transform in portion Laplace Transform of Engineering Mathematics

Answer 1

The correct answer is (a) \(\frac{8s+16}{(s^2+2s-12)^2}\)

The best explanation: In the given question,

L(t e^-2t sinh⁡(4t))

L(sinh⁡(4t))=\(\frac{4}{s^2-16}\)

By effect of multiplication of t

L(t×sinh⁡(4t))=\((-1) \frac{d}{ds} \frac{4}{s^2-16}\)

L(t×sinh⁡(4t))=\(\frac{8s}{(s^2-16)^2}\)

By First shifting property

L(t e^-2t sinh⁡(4t))=\(\frac{8(s+2)}{((s+2)^2-16)^2} = \frac{8s+16}{(s^2+2s-12)^2}\).