The force-deflection equation for a nonlinear spring fixed at one end is F= 4x where F is

The force-deflection equation for a nonlinear spring fixed at one end is F= 4x½ where F is the force, expressed in Newton’s, applied at the other end and x is the deflection expressed in meters.

(a) Determine the deflection x0 if a 100-g block is suspended from the spring and is at rest.

(b) Assuming that the slope of the force-deflection curve at the point corresponding to this loading can be used as an equivalent spring constant, determine the frequency of vibration of the block if it is given a very small downward displacement from its equilibrium position and released.