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The function of time representing a simple harmonic motion with a period of π/ω is

Asked in JEE Main 18th March 2nd Shift 2021 · Identifying SHM

(1) sin(ω t)+cos(ω t)
(2) sin²(ω t)
(3) 3 cos (π/4-2ω t)
(4) cos(ω t)+cos(2ω t)+cos(3ω t)

Answer: (3) 3 cos (π/4-2ω t)

Step-by-step solution

SHM requires a single sine or cosine, and 3 cos (π/4-2ω t) is one cosine of angular frequency 2ω.

Its period is (2π)/(2ω)=π/ω, as asked.

Why the other options are wrong

(1) sin ω t+cos ω t=√2 sin (ω t+π/4) is simple harmonic, but its period is (2π)/ω, twice what is asked.
(2) The period π/ω is right, but sin²ω t is a cosine sitting on a constant, so this paper does not count it as SHM.
(4) A sum of three different frequencies repeats with period (2π)/ω and is not simple harmonic.

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