A mass weighing 2 pounds stretches a spring 0.5 feet. Let y(t) represent the position of the mass at time t seconds, assuming here y is zero at the equilibrium position of the spring-mass system, and that positive (negative) values of y indicate displacement below (above) the equilibrium position. At time zero seconds the mass is released from a point 2/3 feet below the equilibrium position, with an upward speed of 4/3 feet per second. Assuming that there is no damping, write down the differential equation and initial conditions for y, and solve this initial value problem to find the function y(t). Rewrite your solution y(t) in the auxiliary angle form y(t) = A sin(8t - phi), where the phase angle phi is in radians. Use this to find the amplitude of the motion (i.e. the maximum displacement from the equilibrium position) of the spring-mass system, and the time when the mass first passes through the equilibrium position.