Question

The period of the signal X (t) = 10 sin 5t – 4 cos 9t is _______________

(a) \(\frac{24π}{35}\)

(b) \(\frac{4π}{35}\)

(c) 2π

(d) Non-periodic

I got this question in a national level competition.

Query is from Periodic and Non-Periodic Signals topic in portion Signals and Systems Basics of Signals and Systems

Answer 1

Correct option is (c) 2π

To explain I would say: Period of cos t = 2π

Period of cos at = \(\frac{2π}{a}\)

Here, a = 9

So, period of cos 9t = \(\frac{2π}{9}\)

Again, Period of sin t = 2π

Period of sin at = \(\frac{2π}{a}\)

Here, a = 5

So, period of sin 5t = \(\frac{2π}{5}\)

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

∴ Period of X (t) = LCM (\(\frac{2π}{5},  \frac{2π}{9}\)) = 2π.