The equation of motion of a spring-mass system is given by (units: SI system) [500 ddot{x}+1000left(frac{x}{0.025} ight)^{3}=0]

The equation of motion of a spring-mass system is given by (units: SI system)

\[500 \ddot{x}+1000\left(\frac{x}{0.025}\right)^{3}=0\]

a. Determine the static equilibrium position of the system.

b. Derive the linearized equation of motion for small displacements \((x)\) about the static equilibrium position.

c. Find the natural frequency of vibration of the system for small displacements.

d. Find the natural frequency of vibration of the system for small displacements when the mass is 600 (instead of 500).