Use MATLAB for code

S$=$Numerical Value of choice

Problem$-3$:

Consider an excitation force of the form given in figure below. The force is zero until time $t_0,$ when it jumps to a constant level, $F_0.$ This is called the step function, and when used to excite a single$-$degree$-$of$-$freedom system, it might model some machine operation or an automobile

running over a surface that changes level $($such as a curb$).$ The step function of unit magnitude is called the Heaviside step function. Calculate the analytical solution of:

$m{x}^{}+c{x}^{}+kx=F(t)=\{\begin{array}{cc}0,& t_0>t>0\\ F_0,& t{t}_0\end{array}$

Then solve for the response of the system numerically and compare the numerical solution with the analytical solution. Use these parameters in your analysis: $=(s*0\mathrm{.}01+0\mathrm{.}05)$ and ${}_n=3\mathrm{.}16ra\frac{d}{s}($with $F_0=30N,k=(s*4+900)\frac{N}{m},t_0=0).$

Fig: Step function of magnitude $F_0$ applied at time $t=t_0.$