Question

Which of the following functions represents a simple harmonic oscillation?

(a) sinωt-cosωt

(b) sinωt+sin2ωt

(c) sinωt-sin2ωt

(d) sin^2 ωt

This question was addressed to me during an internship interview.

I would like to ask this question from Oscillatory Motion in portion Oscillations of Engineering Physics I

Answer 1

Correct answer is (a) sinωt-cosωt

To elaborate: y=sinωt-cosωt

dy/dt=ωcosωt+ωsinωt

(d^2 y)/dt^2 =-ω^2 sinωt+ω^2 cosωt

=-ω^2 (sinωt-cosωt)

a=-ω^2 y that is a∝y

This satisfies the condition of simple harmonic motion.