The displacement of an object attached to a spring and executing simple harmonic motion is given by x=2×10-2cos(πt) meter . The time at which the maximum speed first occurs is

Given displacement x=2×10-2cos(πt)  velocity is obtained by differentiating above equation,v=dxdt=−2×10−2πsin(πt)For the first time when  v=vmaxsinπt=1sinπt=sinπ2πt=π2T=0.5 seconds.