In the arrangement shown in figure, pulleys are light and spring are ideal. `K_(1)`, `k_(2)`, `k_(3)`and `k_(4)` are force constant of the spring. Calculate period of small vertical oscillations of block of mass `m`.

Answer

A, B, C, D

Explanation

Let block be displacement by x than displacement in springs be
`x_(1),x_(2),x_(3)` and `x_(4)`
Such that `x = 2x_(1) + 2x_(2) + 2x_(3) + 2x_(4)`
Now let restoring force on m be `F = kx` then
`2f = k_(1)x_(1) = k_(2)x_(2) = k_(3)x_(3) = k_(4)x_(4)`
`rArr F/k = (4F)/(k_(1)) + (4F)/(k_(2)) + (4F)/(k_(3)) + (4F)/(k_(4))`
`rArr 1/k = 4(1/(k_(1)) + 1/(k_(2)) + 1/(k_(3) ) + 1/(k_(4)))`

`T = 2pisqrt((m)/(k)) = 2pisqrt(4m(1/(k_(1))+(1)/(k_(2)) + 1/(k_(3)) + 1/(k_(4))))`