The displacement of a particle is represented by the equation  y=5  cos3π2−2π  t  where y is displacement  ω is angular frequency in metre and t is given in instant of  time in h the motion of the particle is

The equation  y=5  cos3π2−2π  t represents simple harmonic motion which takes  the form y=5  sin2π  t+π2 The equation y=5  cos3π2−2π  t  can be  Written asy=5cos⁡2πt−3π2(∵cos⁡(−θ)=cos⁡θ)⇒y=5cos⁡π2+2πt−2π∵3π2=2π−π2⇒y=5cos⁡π2+2πt(∵cos⁡(2π−θ)=cos⁡θ)y=−5sin⁡2πt∵cos⁡π2+θ=−sin⁡θHence time period is 1 hour