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Find the time period of oscillation of b...

Find the time period of oscillation of block of mass m. Spring, and pulley are ideal. Spring constant is k.

A

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

B

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

C

`4pisqrt((m)/(k))`

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
When the block is displaced by `x_(0)`. The spring gets elongated by `2x_(o)`.Since pulley is massles, tension, `T=4kx_(o)`
If the whole set - up is replaceds by a single spring -bloick, then the equivalent spring will be `k_(eq)x_(o)=mgk_(eq)=4k`
therefore Time period, `T=2pisqrt((m)/(k_(eq)))=2pisqrt((m)/(4k))=pisqrt((m)/(k)) `
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