How to convert pen and paper calculation of an ODE to a Matlab/Octave Program

Objective: Assuming we have a spring mass damper system as follows, we know that the ODE of the system will be of the form, `m*((d^2x)/dt^2)+c*(dx/dt)+k*x=0` or `m*x''+c*x'+k*x=0` where, `dx/dt=x' and (d^2x)/dt^2=x''` and if we assume the state variable as `s` then our state space array will be of the of the…