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 initial conditions x$(0)($in m$)$ and x$(0)($in m$/$s$)$ and equations of motion $($in m$)$ if the following situations occur.

$($a$)$

the mass is initially released from rest from a point $1$ meter below the equilibrium position

x$(0)$

$=$ m

x$(0)$

$=$ m$/$s

x$($t$)$

$=$

m

$($b$)$

the mass is initially released from a point $1$ meter below the equilibrium position with an upward velocity of $13$ m$/$s

x$(0)$

$=$ m

x$(0)$

$=$ m$/$s

x$($t$)$

$=$

m