Q. The displacement of a particle along the x-axis is given by x = a sin²ωt. The motion of the particle corresponds to
A) Simple harmonic motion of frequency ω/(2π)
B) Simple harmonic motion of frequency ω/π
C) Simple harmonic motion of frequency 3ω/(2π)
D) Non simple harmonic motion
Explanation
[Solution from source] x = a sin²ωt = (a/2)(1 − cos 2ωt). This is a cosine oscillation of amplitude a/2 about the shifted mean position x = a/2 with angular frequency 2ω, so d²(x − a/2)/dt² = −4ω²(x − a/2): it is SHM of frequency 2ω/2π = ω/π. Calling it non-SHM ignores the shift of the mean position; ω/2π uses the wrong angular frequency. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.