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 sec  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 represents simple harmonic motion  The equation y=5  cos3π2−2π  t  can be  Written asy=5  cos2π t−3π2      ∵cos(−θ)=cosθ   ⇒y=5  cosπ2+2π  t−2π      ∵3π2=2π−π2⇒y=5  cosπ2+2π t         ∵ cos2π−θ=cosθ y=−5  sin2π t             ∵ cosπ2+θ=−sinθ compare with y=Asinωt we get ω=2π we know,  ω=2πT ⇒2πT=2π ⇒T=1 sec time period