Problem #$8$: $($a$)$ A spring$-$mass system moves in free damped motion. The displacement $x(t)$ of the mass is modelled by the

initial value problem

$x^{\text{'}\text{'}}+20x^{\text{'}}+64x=0,x(0)=7,x^{\text{'}}(0)=3.$

Find the displacement $x(t)$ of the mass.

$($b$)$ What is the name of the zero equilibrium point?

Problem #$8($a$)$:

Enter your answer as a symbolic

function of $t,$ as in these

Do not include $\text{'}x(t)=\text{'}$ in your answer.

examples

$($A$)$ nodal sink

$($B$)$ center

$($C$)$ spiral source

$($D$)$ saddle

$($E$)$ nodal source

$($F$)$ spiral sink