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## Homework Statement

The ordinary differential equation describing shm is

d^2x/dt^2=-w^2x

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

## Homework Equations

k1=hf(xn,yn)

k2=hf(x+h, y+k1)

y_(n+1)=y_n+(1/2)k_1+(1/2)k_2

## 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.