A mass m = 2 kg is attached to a spring with a spring constant of k = 8 kg/s2. There is no damping on the system. The mass is pulled down 1/4 meter and released, with no velocity imparted at the time of release.
(a) Suppose there is no external force applied to the system. Find the function y(t)
that gives the position of the mass at time t seconds.
(b) What is the natural frequency ω0 of the system?
(c) What is the maximum distance the mass will travel from its equilibrium position?
(d) Find the first time t that the mass returns to its equilibrium position.