Question

The period of the signal Z (t) = sin3t + cos 4t is _______________

(a) periodic without a definite period

(b) periodic with a definite period

(c) non- periodic over an interval

(d) non-periodic throughout

The question was posed to me in a dream while sleeping

Question is from Periodic and Non-Periodic Signals in division Signals and Systems Basics of Signals and Systems

Answer 1

Correct answer is (b) periodic with a definite period

To elaborate: Period of cos t = 2π

Period of cos at = \(\frac{2π}{a}\)

Here, a = 4

So, period of cos 4t = \(\frac{2π}{4}\)

= \(\frac{π}{2}\)

Again, Period of sin t = 2π

Period of sin at = \(\frac{2π}{a}\)

Here, a = 3

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

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

∴ Period of X (t) = LCM (\(\frac{2π}{5}, \frac{2π}{4}\)) = definite

Hence Z (t) is periodic with a definite period.