The force-deflection equation for a nonlinear spring fixed

Chapter 19, Problem 19.32

(choose chapter or problem)

The force-deflection equation for a nonlinear spring fixed at one end is \(F = 1.5x^{1/2}\) where F is the force, expressed in newtons, applied at the other end and x is the deflection expressed in meters. (a) Determine the deflection \(x_{0}\) if a 4-oz 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.