A 1-kilogram mass is attached to a spring whose constant is 27 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 12 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 -3t +C₂e x(t) = -9t C₁e 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) = m

A 1-kilogram mass is attached to a spring whose constant is 27 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 12 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 -3t +C₂e x(t) = -9t C₁e 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) = m