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 . Hence from the equation y=10sin40t+π2 , ω1=40   rad/s and from  the equation  y=10cos25t+π4, ω2=25  rad/s , Using the relation  ω=2πT , ω1ω2=T2T1  ,Hence T1T2=ω2ω1=2540=58Solving the above fraction we get  T1T2=58=0.825.