A 1-kilogram mass is attached to a spring whose constant is 24 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 11 times the instantaneous velocity. Determine the equations of motion if the following is true.

(a) the mass is initially released from rest from a point 1 meter below the equilibrium position x(t) = -3/5 e^-8t + 8/5 e^-3t m (b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 11 m/s x(t) 2e^-8t -e^-3t m