A particle executes simple harmonic motion with a time period of 16s. At time t = 2s, the particle crosses the mean position while at t = 4s, its velocity is 4 ms-1. The amplitude of motion in meter is

At t=2sec, the particle crosses mean position.  At t=4sec , its velocity is 4 ms−1 For simple harmonic motion, y=asin(ωt+ϕ)∴y=asin((2πT)t+ϕ)⇒0=asin[(2π16)×2+ϕ]⇒π4+ϕ=0 ⇒ϕ=−π4y coordinate at t=4s isy=asin((2π16)4−π4)=a2Now, v=ωa2−y2⇒4=2π16a2−a22⇒a=322π