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A particle of mass m is attached with th...

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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Text Solution

Verified by Experts

The correct Answer is:
A
`OP = x`
`/_ POM = /_ PON ~~ 45^(@)`
`y = xcos 45^(@) = (x)/(sqrt2)`
Net restoring force,
`F_(net) = - [kx + 2ky cos 45^(@)]`
` = - (2k)x (as y = (x)/(sqrt2))`
`:. k_(e) = 2k`
Now, `T = 2pi sqrt((m)/(k_(e)) = 2pi sqrt((m)/(2k))`.
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