The following figure shows a particle of mass, `m`, attached with four identical springs, each of length `l`. Initial tension in each spring is `F_(0)`. The period of small oscillations of the particle along a line perpendicular to the plane of the figure is (neglect gravity)

Options

A. `pi sqrt((ml)/(F_(0)))`
B. `2pi sqrt((ml)/(F_(0)))`
C. `2pi sqrt((ml)/(2F_(0)))`
D. `pi sqrt((ml)/(4F_(0)))`

Answer

A

Explanation

Let `x` is the small displacement from mean position perpendicuar to plane of figure then:

restroing force on particle due to only two springs `=2 (F_(0) +dF_(0)) sin theta`, From symmetry, total restoring force due to all four springs =
`4(F_(0) +dF_(0)) sin theta: ~~4 (F_(0) +dF_(0)) (x)/(l)`
`~~(4F_(0))/(l)x ( :' dF_(0).x rarr0) rArr a =- (4F_(0))/(ml)x =- omega^(2)x`
`:. T = (2pi)/(omega) =`