A $1$ kg mass is attached to spring whose constant is $16\frac{(N)}{(m)},$ and the entire system is submerged in a liquid that imparts a damping force numerically equal to $10$ times the instantaneous velocity. Determine the equation that gives the location of the mass as a function of time if

a$)$ the mass is released from rest from a point $1$ m below the equilibrium position.

b$)$ the mass is released from a point $1$ m below the equilibrium position with an upward velocity on $12\frac{(m)}{(s)}.$

Please solve step by step