A 0.60kg mass hangs from a vertical spring and oscillates up and down with negligible air resistance. When the mass is attached and allowed to hang at rest, the spring stretches 0.25m relative to its natural (unstretched) length. The mass is then pulled downward an additional 0.12m from its equilibrium position and released from rest.
(a) Determine the force constant k of the spring.
(b) Calculate the speed of the mass when it is moving upward and is 0.06m above the equilibrium position.
(c) During its first upward excursion, the mass eventually comes instantaneously to rest at its highest point. Determine that highest vertical position relative to equilibrium and explain your method.
(d) Discuss how the interplay among elastic potential energy, gravitational potential energy, and kinetic energy governs the motion of the mass throughout one complete oscillation.