Question

A particle has an equation of motion given by: x = cos^2wt – sin^2wt. Select the correct statement regarding the same.

(a) It is not a SHM

(b) It is a SHM with T = π/w

(c) It is an SHM with T = 2π/w

(d) Amplitude of motion is 1/√2 m

I got this question in an international level competition.

The query is from Simple Harmonic Motion topic in chapter Oscillations of Physics – Class 11

Answer 1

Right answer is (b) It is a SHM with T = π/w

The best explanation: x = cos^2wt – sin^2wt = cos 2wt.                                                                                                                 Thus, time period T = 2π/2w = π/w.                                                                                                   Also the amplitude of motion is 1m.