The displacement of a particle is represented by the equation y=3cosπ4-2wt. The motion of the particle is

Given  y=3cosπ/4-2wtVelocity  V=dydt=ddt3cosπ/4-2wt=3(-2w)-sinπ/4-2wtV=6wsinπ/4-2wtAcceleration a=dVdt=ddt6wsinπ/4-2wt =6w×-2wcosπ/4-2wt=−12w2cosπ/4-2wt=−4w23cosπ/4-2wta=-4w2yaα-y.Hence, due to negative sign motion is SHM.Clearly, from the equation w1=2w [standard equation y=acos(wt+ φ )]2πT1=2wT1=πw. So motion is SHM with period π/w .