Question

The period of the signal X (t) = 5t – 2 cos 6000 πt is ________________

(a) 0.96 ms

(b) 1.4 ms

(c) 0.4 ms

(d) Non-periodic

This question was addressed to me in semester exam.

The question is from Periodic and Non-Periodic Signals topic in division Signals and Systems Basics of Signals and Systems

Answer 1

Correct answer is (d) Non-periodic

To explain: Period of cos t = 2π

Period of cos at = \(\frac{2π}{a}\)

Here, a = 6000π

So, period of cos 6000πt = \(\frac{2π}{6000π}\)

= \(\frac{1}{3000}\)

Again, Period of t = indefinite

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

∴ Period of X (t) = LCM (\(\frac{1}{3000}\), ∞) = Indefinite.