Question

The displacement of particle in S.H.M. may be given by y = a sin (ωt + φ) show that if the time t is increased by 2π/ω, the value of y remains the same.

Answer 1

The displacement at any time t is 

 y = a sin (ωt + φ) 

. ^.. displacement at any time (t + 2π/ω) will be 

y = a sin [ω (t + 2π/ω) + φ] = [sin {ωt + φ) + 2π}] 

y = a sin (ωt + φ) [. ^.. sin (2π + φ) = sin φ] 

Hence, the displacement at time t and (t + 2π/ω) are same.