Question

The period of the signal X (t) = 4 sin 6t + 3 sin \(\sqrt{3}\)t is ________________

(a) \(\frac{2π}{3}\) s

(b) \(\frac{2π}{\sqrt{3}}\) s

(c) 2π s

(d) Non-periodic

I got this question in an online quiz.

This intriguing question originated from Periodic and Non-Periodic Signals topic in chapter Signals and Systems Basics of Signals and Systems

Answer 1

Correct option is (d) Non-periodic

Explanation: Period of sin t = 2π

Period of sin at = \(\frac{2π}{a}\)

Here, a = 6

So, period of sin 6t = \(\frac{2π}{6}\)

Again, a = \(\sqrt{3}\)

So, period of sin \(\sqrt{3}\)t = \(\frac{2π}{\sqrt{3}}\)

∴ Period of X (t) = LCM [Period of X1 (t), Period of X2 (t)]

∴ Period of X (t) = LCM (\(\frac{π}{3},  \frac{2π}{\sqrt{3}}\)) = Indefinite.