Q. Out of the following functions representing motion of a particle which represents SHM?
A) Only y = sin ωt − cos ωt and y = sin³ωt
B) Only y = sin ωt − cos ωt
C) Only y = 1 + ωt + ω²t² does not represent SHM
D) Only y = sin ωt − cos ωt and y = 5 cos(3π/4 − 3ωt)
Explanation
[Solution from source] sin ωt − cos ωt = √2 sin(ωt − π/4) and 5 cos(3π/4 − 3ωt) are single sinusoids, so both are SHM. sin³ωt = (3 sin ωt − sin 3ωt)/4 is periodic but a mix of two frequencies, so not SHM, and 1 + ωt + ω²t² is not even periodic. So only the first and third functions are SHM; the claim that only the last function fails is wrong because sin³ωt also fails. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.