The equation of motion of a system is given by

$M{L}^2{}^{}+(KL{L}^2-MgL)=0$

Take $K=250\frac{N}{m},$ and $M=100kg,L=20m.$

Determine: natural frequency.

Determine: $($a$)$ the equivalent spring stiffness for the systems shown, and

$($b$)$ the natural frequency.