The general solution to

$\frac{dx}{dt}=y$

$\frac{dy}{dt}=-2x-2y$

is

$x(t)=c_1{e}^{-t}cos(t)+c_2{e}^{-t}sin(t)$

$y(t)=c_1{e}^{-t}(-cos(t)-sin(t))+c_2{e}^{-t}(-sin(t)+cos(t))$

Which part$($s$)$ of the general solution accounts for the fact that the differential equations predict that the mass will oscillate about the zero position? Which part$($s$)$ of the general solution accounts for the fact that the amplitude of the oscillations decreases over time?