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.

Answer

2

Explanation

Initial stretch in both springs `= d - (3d)/(4) = (d)/(4)`
`F_(restoring) = k((d)/(4)+x) -k ((d)/(4)-x) = 2kx = omega_(1)^(2) x`

`d^(1) = d sec theta, :. X' = d sec theta - (3d)/(4)`
force towads equilibrium position `=(kx' sin theta)`, due to one spring `=2(kx' sin theta)`, due two springs for small `theta`, force `= k ((d.theta)/(2)) = omega_(2)^(2) theta rArr (T_(B))/(T_(A)) = 2`