$KE \ = \ \frac{1}{2} \ Io \ \theta^2$

$= \frac{1}{2} \ [ IG \ + \ m (disp)^2] \ \theta^2$

$= \frac{1}{2} \ [ \frac{mL^2}{12} \ + \ m \ (\frac{L}{4})^2 ] \ \theta^2$

$I_{eq} \ = \ \frac{mL^2}{12} \ + \ \frac{mL^2}{16}$

$PE \ = \ \frac{1}{2} \ k \ ( \frac{L}{4} \ \theta) ^ 2$

$= \frac{kL^2}{16}$

$W.D = - \int c.y dy$

$y = \frac{3L}{4} \theta$

$\dot{y} = \frac{3L}{4} \dot{\theta}$

$\therefore$ $W.D. \ = \ - \int \ c \ [ \frac{3L}{4} \dot{\theta}] \ d \ [ \frac{3L}{4} \theta]$

$= \ - \int \ c \ \frac{9L^2}{16} \ \dot{\theta} d \ \theta$

$\therefore$ $C_{eq} \ = \ \frac{9cL^2}{16}$