Question

In SHM projection of uniform circular motion
of a uniformly revolving particle on a circle, having
Sense of rotation clock wise can be represented as
x = 2 sin ( 2t + π/3) where x in cm and t in s. The
initial phase and period of revolution of particle is​

Answer 1

Given info : In SHM projection of uniform circular motion of a uniformly revolving particle on a circle, having Sense of rotation clock wise can be represented as x = 2 sin ( 2t + π/3) where x in cm and t in s.

To find : initial phase and period of revolution of particle are...

solution : equation of SHM is , x = 2 sin(2t + π/3)

initial phase, Φ₀ = value of (2t + π/3) at t = 0

= π/3 or 60°

as we know from standard equation of SHM , x = Asin(ωt + Φ₀)

on comparing we get, ω = 2 rad/s

but angular frequency, ω = 2π/T = 2

⇒T = π sec

Therefore period of revolution is π sec.

Answer 2

The initial phase is

π/3 = 180°/3 = 60°

time period of revolution = π seconds