A small body of mass `m` is connected to two horizontal spring of elastic constant `k`, natural length `(3d)/(4)`. In the equilibrium position botgh springs are stretched to length `d`, as shown in Fig. What will be the ratio of perod of the motion `((T_b)/(T_a))` If the body is displaced horizontally by a small distance where `T_a` is the time period when the particle owscillates along the line of spring `T_b` is time plane of the figure? Neglect effect of gravity.

Explanation

Initial stretch in both springs `=d-(3d)/(4)=(d)/(4)`
`f_(resteri ng)=k((d)/(4)_x)-k((d)/(4)-x)=2kx`
`impliesT_a=2pisqrt((m)/(k))`
`d'=dsectheta`
`x'=dsectheta-(3d)/(4)=d((1)/(costheta)-(3)/(4))`