A 0.50kg block is attached to a horizontal spring. The restoring force developed in the spring as the block is displaced is found experimentally to be
F=−100x−50x3,
where F is in newtons and x in metres, the origin being the equilibrium position.
(a) Show that, for small oscillations in which ∣x∣ is sufficiently small, the motion of the block can be treated as simple harmonic.
(b) Under the approximation made in part (a), obtain the angular frequency and the time period of the motion.
(c) Estimate the maximum displacement xmax for which the magnitude of the nonlinear term 50x3 remains less than 5% of the linear term 100x.