Need analyze the periods the individual signals

Solved Step by Step With Explanation- Periodicity of Summed Signals

Questions

Three periodic signals x(t) = cos(2t),x2(t) = cos(√5 t), and x3 (t) = 3 sin(4t) are summed to form signal v(t). Test if the signal v(t) is periodic and if yes, find its period. [11 points]

Answers

Given:

x1(t) = cos(2t) (angular frequency ω1 = 2)

T2 = 2π / ω2 = 2π / √5

T3 = 2π / ω3 = 2π / 4 = π/2

LCM(π, 2π√5 / 5, π/2) = LCM(π, 2π√5, π/2) / 5

Now, we need to find the LCM of π, 2π√5, and π/2. Since π is a common factor of all three terms, the LCM will be the largest of the three terms: