A particle executes a S.H.M. of amplitude 20 cm and period 3 s. What is the minimum time required by the particle to move between two points 10 cm on eith side of the mean position ?

Options

A. 1 s
B. `(3)/(4)s`
C. `(1)/(2)s`
D. `(1)/(4)s`

Answer

C

Explanation

`x=A "sin" omega t= A "sin" ((2pi)/(T))t`
`therefore 10 =20 "sin" ((2pi)/(3))t`
`therefore "sin" ((2pi)/(3))t =(10)/(20)=(1)/(2)="sin"(pi)/(6)`
`therefore (2pi)/(3)t =(pi)/(6) therefore t =(1)/(4)s`
Time taken by the particle to move between two points 10 cm on either side of the mean position `=2t=(1)/(2)s`