A particle of mass `m` is attached with three springs `A,B` and `C` of equal force constancts `k` as shown in figure. The particle is pushed slightly against the spring `C` and released. Find the time period of oscillation.
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Explanation

Let spring C is compressed by distance x

Spring B and C each are extended `x/sqrt2`
Restoring force on block

Restoring force on block
`F=-[kx+sqrt(((kx)/(sqrt2))^2+((kx)/(sqrt2))^2)]=-2kx`
`-2kx=ma`
`a=-(2k)/(m)x=-omega^2x`
`T=2pisqrt((m)/(2k))`