1. A mass m on a vertical spring with force constant k has an amplitude of A. Using the top of the motion as the origin for both gravitational potential energy and spring potential energy: (a) Find an expression for the maximum and minimum gravitational potential energy of the system. (b) Find an expression for the maximum and minimum spring potential energy of the system. (c) At what location is kinetic energy a maximum? Use this information to find an expression for the maximum kinetic energy of the spring without using velocity or position.