A particle executes SHM with amplitude 0.2 m and time period 24 s . The time required for it to move from the mean position to a point 0.1 m from the mean position is

Options

A. 2 s
B. 3 s
C. 8 s
D. 12 s

Answer

A

Explanation

Here ,
Amplitude , A = 0.2 m
Time period , T = 24 s
Since time is noted from the mean position , hence displacement x of a particle from its mean position is given by
x = A `sin omega t`
Here , `x = 0.1 m " " therefore 0.1 = 0.2 sin omega t`
`(1)/(2) = sin omega t`
`sin ((pi)/(6)) = sin omega t`
`omega t = (pi)/(6)`
`t = (pi)/(6 omega) = (pi)/(6) ((T)/(2pi)) " " (because omega = (2pi)/(T))`
`= (pi xx 24 )/(6 xx 2pi ) = 2 s`