With the position $x(t)$ and the velocity $v(t)=dx/dt$ we can reformulate Newton's equation in the following way $$\frac{dx(t)}{dt}=v(t),$$ and $$\frac{dv(t)}{dt}=-\omega_0^2x(t).$$ We are now going to solve these equations using the Runge-Kutta method to fourth order discussed previously.