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

Options

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

Answer

B

Explanation

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)))`