1. A 10-kg mass attached to a spring with stiffness 250 N/m, with negligible resistance. Initially,
the string is contracted by 15 cm relative to its natural length and the mass is moving outward
(i.e. towards the equilibrium position) at 1 m/sec.
(a) Sketch a diagram, indicate the variables and units and state differential equation and
the intial conditions for $x(t)$, the position of the mass as a function of time.
(b) Determine an explicit formula for $x(t)$ and the amplitude of the resulting oscillations.
Include the appropriate units.
(c) Use the formula in part b to find the earliest positive time when the direction of mo-
tion reverses from outward to inward (equivalently, the string is stretched as much as
possible).
