A particle moves on x-axis according to the equation x=x0sin2wt, the motion is simple harmonic,
with amplitude 2x0
x=x0 sin2ωt
=x02(1−cos 2ωt)=x02−x02cos 2ωt
Frequency ω′=2ω
⇒2πT′=2ω
⇒T′=(πω)
Amplitude=x02