The ordinary differential equation describing shm is
where x is the displacement, t is the time and w is the frequency. If x=0 at t=0, the analytical solution is x=Asin(wt), where A is the amplitude.
1) Rewite equation 1 as two first oder ode's suitable for solution using Runge Kutta Methods
2)Determine the second order runge-kutta solution for this system after the first time step h and show the leading error term in x(h) is proportional to h^3
The Attempt at a Solution
I have completed part 1 and got dx/dt=v and dv/dt=-w^2x but I am unsure how to proceed. The lecturer didn't do a great job of explaining the method and I don't know how to do it when you have two equations and are not given the step size.