The initial position and velocity of a body moving in SHM with period `T = 0.25s` are `x = 5.0cm` and `v = 218cm//s`. What are the amplitude and phase constant of the motion ?

Answer

A, C, D

Explanation

`omega = (2pi)/(T) = (2pi)/(0.25) = (8pi)rad//s`
`x = A sin(omega t + phi)`
`U = (dx)/(dt) = omega A cos (omega t + phi)`
At `t = 0`
`x = Asin phi`
`:. 5 = A sin phi` ...(i)
`U = omega A cos phi = (8pi) A cos phi`
`:. 218 = (8pi A)cos phi` ...(ii)
Solving Eqs. (i) and (ii) we get,
`A = 10 cm` and `phi = (pi)/(6)` or `30^(@)`