A light rod AB is fitted with a small sleeve of mass m which can slide smoothly over it. The sleeve is connected to the two ends of the rod using two springs of force constant 2k and k (see fig). The ends of the springs at A and B are fixed and the other ends (connected to sleeve) can move along with the sleeve. The natural length of spring connected to A is `l_(0)`. Now the rod is rotated with angular velocity w about an axis passing through end A that is perpendicular to the rod. Take `(k)/(momega^(2)) = eta` and express the change in length of each spring (in equilibrium position of the sleeve relative to the rod) in terms of `l_(0)` and `eta`.

Answer

`x = (l_(0))/(3eta-1)`