$(150$ XPs$)$ The differential equation for a mass$-$spring$-$damper system is given below as well as the parameters. Find the following.

a$.$ The number of $-$groups

b$.$ A complete set of $-$groups

$[x]=L,m\frac{d^{2}x}{d{t}^2}+d\frac{dx}{dt}+kx=F$

$[d]=\frac{M}{T},x(0)=x_0$

$[k]=\frac{M}{T^2},$

$[F]=M\frac{L}{T^2},$

$[m]=M,\frac{dx}{dt}{|}_t||=0=v_0$

$[x_0]=L,$

$[v_0]=\frac{L}{T},$

$[t]=T,$

Solve thoroughly