# 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 x(t)=_________________________________________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

Question

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

x(t)=_________________________________________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