iii) The free vibration of an undamped nonlinear oscillator is given in the form: mž + R(z) = 0 Derive an expression for the oscillator period when R(z) is a symmetric function, and use it to obtain the period for a maximum oscillation amplitude of 0.2 m, when the mass m=10 kg, and the nonlinear stiffness conforms to the model: R(z) = a z> 0 -a z<0 where the constant a=100 N.