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A particle of mass 'm' is attached to th...

A particle of mass 'm' is attached to three identical springs `A,B` and `C` each of force constant 'K' as shown in figure. If the particle of mass 'm' is pushed slightly against the spring 'A' and released the period of oscillations is

A

`2pisqrt((2m)/(k))`

B

`2pisqrt((m)/(2k))`

C

`2pisqrt((m)/(k))`

D

`2pisqrt((m)/(3k))`

Text Solution

Verified by Experts

The correct Answer is:
B
(b)
`OO'=x`(say)
Then `O'M=O'N~~(x)/(sqrt(2))`
i.e., elongation in spring B and `x//sqrt(2))` , while compression in spring A is x.
Net restarting force
`F=-[kx+(2kx)/(sqrt(2))"cos"45^(@)]=-2kx`
`therefore a=(F)/(m)=-(2k)/(m)x`
`T=2pisqrt(|(x)/(a)|)=2pisqrt((m)/(2k))`
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