Which of the following functions of time represent periodic motion. For theones   which are periodic, find the time period.(i) cos2ωt+sin5ωt   (ii)  sin22ωt

cos2ωt+sin5ωt As per Fourier theorem, cos2ωt+sin5ωt  is a periodic function. Time period of cos2ωt  is T1=2π2ω  . Time period of sin5ωt is  T2=2π5ωIts time period is the LCM of  T1 and T2 , which is  2πω.sin22ωt=12−cos4ωt2 It is a periodic function with time period =  2π4ω=π2ω