Two. S.H.M’s are represented by the relations  y=10sin40t+π2 and y=10cos25t+π4  . Then the ratio of their time periods is

We can compare the given two equations with the standard equation  y=Asinωt+ϕ .----(1) Hence from the equation  y=10sin40t+π2, on comparing with above equation(1) => ω1=40   rad/s and  y=10cos25t+π4=10sin25t+π4+π2=10sin25t+3π4, on comparing with standard equation (1)=>ω2=25  rad/s , from the relation   ω=2πT,  ω1ω2=T2T1 ,Hence  T1T2=ω2ω1=2540=58Solving the above fraction we get  T1T2=58=0.625.