A particle  execute SHM from the mean position. Its amplitude is A, its time period is ‘T’. At what displacement, its speed is half of its maximum speed.

given oscillator speed is V=12Vmax                                                =12Aω.........(1)   where maximum velocity Vmax=Aω oscillator velocity is V=ωA2-Y2---(2) substitute (1) in (2)  12Aω=ωA2-Y2 ⇒ 12A=A2-Y2  ⇒14A2=A2-Y2 ⇒ Y2=A2−A24  ⇒ Y2=3A24 ⇒Y=3A2