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

Options

A. (a)`2pisqrt((m)/(k))`
B. (b)`pisqrt((m)/(k))`
C. (c)`4pisqrt((m)/(k))`
D. (d)`2pisqrt((m)/(2k))`

Answer

B

Explanation

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)) `