$(10$ points$)$ In Sympy solve the initial value problem for a damped harmonic oscillator

$m{y}^{\text{'}\text{'}}+c{y}^{\text{'}}+ky=g(t),y(0)=0\mathrm{.}05,y^{\text{'}}(0)=0.$

for $m=2,k=30,c=0\mathrm{.}6$ and $g=0.$ Plot the resulting solution for tin$(0,30),$ and classify the motion as underdamped,

critically damped, or overdamped.

Repeat with the same values of $m,k,c,$ but with $g(t)$ changed to:

$($a$)g(t)=4cos(2t)$

$($b$)g(t)=4cos(4t)$

$($c$)g(t)=4cos(6t)$

Which gives the largest amplitude?