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In the given figure pulleys and strings ...

In the given figure pulleys and strings are ideal. The time period of (Assume that string remains taut) vertical oscillations of the block is,

A

`pisqrt((m(K_(2)+4K_(1)))/(K_(1)K_(2)))`

B

`(pi)/2sqrt((m(K_(2)+4K_(1)))/(K_(1)K_(2))`

C

`2pisqrt((m(K_(1)+K_(2)))/(K_(1)K_(2))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Suppose extension in two spring are `x_(1)` and `x_(2)`
Displacement of block
`x=(x_(2))/2+(x_(1))/4`
`2K_(1)x_(1)=K_(2)x_(2)=F/2`
`1/(K_(eq))=1/(16K_(1))+1/(4K_(2)),K_(eq)=(16K_(1)K_(2))/(4K_(1)+K_(2))`
`T=2pi sqrt((m(4K_(1)+K_(2)))/(16K_(1)K_(2))),T=(pi)/2 sqrt((m(4K_(1)+K_(2)))/(K_(1) K_(2)))`
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