As shown in figure in a simple barmonic motion obscillator having identical four springs has time period

Options

A. `T = 2 pi sqrt((m)/(4 k))`
B. `T = 2 pi sqrt((m)/(2 k))`
C. `T = 2 pi sqrt((m)/( k))`
D. `T = 2 pi sqrt((m)/(8 k))`

Answer

c

Explanation

`k_(1)` and `k_(2)` parallel and `k_(3)` and `k_(4)` are parrallel .The two combnations an in same with each other
`k_(1) + k_(2) = 2k`
`k_(3) + k_(4) = 4k`
`(1)/(k_(eq)) = (1)/(2k) + (1)/(2k)`
`k_(eq) = k`
`T = 2 pi sqrt((m)/(k))`