A particle performing simple harmonic motion undergoes unitial displacement of `(A)/(2)` (where A is the amplitude of simple harmonic motion) in 1 s. At `t=0`, the particle may be at he extreme position or mean position the time period of the simple harmonic motion can be

Options

A. `12s`
B. `2.4`
C. `6s`
D. `1.2s`

Answer

A, B, C, D

Explanation

A particle ……….
It `T` be time period : time to go from `O` to `Q` is `(T)/(12)` and from `M` to `P` is `(T)/(6)` .

The displacement is when particle goes from `O` to `Q` , from `O` to `N` to `Q` , from `O` to `N` to `P`, and so on
`:. t = (T)/(12) or t = (T)/(4)+(T)/(6)= (5T)/(12)`
or `t = (T)/(2)+(T)/(12)=(7T)/(12)`
Hence possible time period `T` is
`T = 12s` or `T = (12xx1)/(5)=2.4s`
or `T = (12xx1)/(7)s`1
similarly displacement is `(A)/(2)` when particle goes from `M` to `P` or `M` to `N` to `P`
Hence the possible time period `T = (6)/(5)xx1= 1.2 s`
`T = 1xx6=6s` or `T = 1.2s`
`T = 1.2s, 6s, 2.4s, 12s`