Question

Given signal given, \( y (t) = 2sin (\frac{2}{3} t) + 4sin (\frac{1}{4} t – \frac{π}{4}) + 6sin⁡ (\frac{1}{3} t – \frac{π}{5}) + 8sin⁡ (\frac{1}{2} t – \frac{π}{7}\)). The period of y(t) is ________________

(a) 12 π

(b) 24 π

(c) 8 π

(d) 16 π

This question was posed to me in class test.

I'm obligated to ask this question of Average Power and Energy of a Signal topic in division Fourier Series of Signals and Systems

Answer 1

Right option is (b) 24 π

The explanation is: ω1 =  \(\frac{2}{3}\)

Or, T1 = \(\frac{2π}{ω_1}\) = 3π

Again, ω2 =  \(\frac{1}{4}\)

Or, T2 = \(\frac{2π}{ω_2}\) = 8π

Again, ω3 =  \(\frac{1}{3}\)

Or, T3 = \(\frac{2π}{ω_3}\) = 6π

And, ω4 =  \(\frac{1}{2}\)

Or, T4 = \(\frac{2π}{ω_4}\) = 4π

∴ T = LCM (3π, 8 π, 6π, 4π)

∴ T = 24π.