(Solved): (a) If x(t) is a solution to a damped unforced mass-spring oscillator equation, then x(t)0, as t ...

(a) If $x(t)$ is a solution to a damped unforced mass-spring oscillator equation, then $x(t)?0$, as $t??$. ALWAYS SOMETIMES NEVER (b) If $V$ is a non-zero vector in the plane, then $X(t)=e^{?t^2}V$ is a solution to the planar linear system $X^{?}=AX$. ALWAYS SOMETIMES NEVER (c) If $X(t)=\left[\begin{array}{l}x(t)\\ y(t)\end{array}\right]$ is a solution to the system $X^{?}=AX$, then $x(t{)}^2+y(t{)}^2??$, as $t?10^{10}$. ALWAYS SOMETIMES NEVER (d) If $D=1+T^2$, where $D=\det (A)$ and $T=\mathrm{trace}(A)$, and $A$ is a $2\times 2$ matrix, then the phase portrait of the system $X^{?}=AX$ is a saddle. ALWAYS SOMETIMES NEVER (e) If $x(t)$ is a solution to a forced mass-spring oscillator equation with forcing equal to $f(t)=$ ${?}_{2023}(t)$ and $x(0)=x^{?}(0)=0$, then $x(2022)>0$.