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.