### The Action of a Harmonic Oscillator

Consider the harmonic oscillator, for which the general solution is x(t) = A cos(wt) + B sin(wt) 1. Express the energy in terms of A and B and show it is time independent. 2. Choose A and B such that x(0)=x1 and x(T)=x2. 3. Write down the energy in terms of x1, x2 and T. 4. Calculate the action S for the trajectory conn