A block of mass 0.40kg is attached to a horizontal spring of force constant 80Nm−1 on a frictionless surface. The block is released from rest when the spring is compressed 0.20m from its equilibrium length.
(a) Derive an expression for the speed v(x) of the block as a function of its displacement x from equilibrium during the subsequent motion, in terms of the given quantities.
(b) Using a carefully labeled sketch of the spring’s potential energy U versus displacement x (from x=−0.20m to x=0.20m), indicate on the graph the point(s) where the block’s speed is maximum and where it is zero. Explain how the graph supports your identification.
(c) Calculate the speed of the block when its displacement is x=0.15m.