Construct a MATLAB program to implement $4^{th}$ order $R-K$ Method to solve the following initial value

problem

$m{x}^{}+c{x}^{}+kx=cos3t$

Use $m=1,c=2,k=4.$ Solve for initial velocity, $x^{}(0)=0$; and an initial displacement, $x(0)=1.$

Plot displacement vs time. Use an appropriate time step and end time to capture the dynamics of the

system.

Note that the $2^{nd}$ order equation can be converted in to two first order equations, using a newly defined

set of "state variables" $x_1=x$ and $x_2=x^{}$

$x_1^{}=x_2$

$x_2^{}=cos3t-2x_2-4x_1$