Compute the general response $($homogenous response $+$ forced response$)$ of a spring$-$mass system with the following values: $m=4kg,k=676\frac{N}{m},$ subject to a harmonic force $($cosine$)$ of magnitude $F0=80N$ and frequency of $5ra\frac{d}{s}.$ The inital conditions are $0=0\mathrm{.}01m$ and $v_0=0\mathrm{.}01\frac{m}{s}.$ Complete following steps.

a$.$ Equation of motion

b$.$ Forced response solution xp

c$.$ Homogenous response solution xh as affected by external force and initial conditions

d$.$ Total response $x(t)=xh+xp$

e$.$ Plot $x(t)($use excel or MATLAB$)$