# Answer to Question #129881 in Electrical Engineering for Md.Mostafijur Rahman

Question #129881
Determine whether the following signals are periodic or non periodic if the signal is periodic find the fundamental period of
1. x (t) = 6cos 5/4 t + 2 cos 9/7 t
2. x (t) = sin√3t +cos √3t
1
2020-08-20T04:34:13-0400

Consider the function

"x (t) = 6\\text{cos} \\bigg(\\frac{5}{4}t\\bigg) + 2 \\text{cos }\\bigg(\\frac{9}{7} t\\bigg)."

This function is periodic with a period of 175.9

To avoid ambiguity, consider two functions as a second function:

"2.1\\space\\space x(t)=\\text{sin}(\\sqrt3\\cdot t)+\\text{cos}(\\sqrt3\\cdot t),\\\\\n2.2\\space\\space x(t)=\\text{sin}(\\sqrt{3t})+\\text{cos}(\\sqrt{3t})."

The first one is a periodic function with a period of

"T=\\frac{2\\pi}{\\sqrt3}\\approx3.63."

How did we find it? Simplify the sum of a sine and cosine of the same argument, you get

"f(t)=\\text{sin}(kt)+\\text{cos}(kt)=\\sqrt2\\text{ sin}\\bigg(kt+\\frac{\\pi}{4}\\bigg)."

This is a simple sine function that is certainly periodic. The period of a periodic function is

"T=\\frac{2\\pi}{k}."

The function 2.2 is not a periodic function.

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