As shown in figure in a simple harmonic motion oscillator having identical four springs has time period

Options

A. `T=2pisqrt((m)/(4k))`
B. `T=2pisqrt((m)/(2k))`
C. `T=2pisqrt(m/k)`
D. `T=2pisqrt((2m)/(k))`

Answer

C

Explanation

The upper two springs are in parallel,
`(k_1)_(eq)=k+k=2k`
The lower two springs are in parallel,
`(k_2)_(eq)=k+k=2k`
`(k_1)_(eq)` and `(k_2)_(eq)` are in series
`k_(eq)=(2k*2k)/(2k+2k)=k`
`T=2pisqrt((m)/(k_(eq)))=2pisqrt(m/k)`