Question

A particle moves on the X-axis according to the equation x=x_o sin² ωt. The motion is simple harmonic

(a) with amplitude x_o

(b) with amplitude 2x_0​

(c) with time period 2π/ω 

(d) with time period π/ω 

Answer 1

(d) with time period π/ω.

EXPLANATION:  

x = x₀sin²⍵t =x₀(1-cos2⍵t)/2 →x = x₀/2 - ½x₀.cos2⍵t. 

It gives the amplitude as x₀/2, hence (a) and (b) are not true. The time period is given as T=2π/(2⍵) =π/⍵. So (d) is true not (c).