Project #$2-$ Adaptive Runge Kutta

The differential equation describing the motion of the mass$-$spring$-$dashpot system is

$y^{\text{'}\text{'}}+cm{y}^{**}+kmy=0$ where

$m=5kg,c=460N*\frac{s}{m},$ and $k=450\frac{N}{m}.$

The initial conditions are $y(0)=0\mathrm{.}01m$ and $y(0)=0.$

Integrate the initial value problem specified with the adaptive Runge$-$Kutta method from

$t=0$ to $0\mathrm{.}2s,$ and plot $y^{**}$ versus $t.$

For this purpose, develop a Matlab program to implement.

You should use Matlab software.

All code should be fully commented and clear.

Do not use Matlab built$-$in functions.

You should verify your code using an alternative method