Energy in a block on a spring

A $0.50\ \text{kg}$ block on a smooth floor is tied to a spring with $k = 180\ \text{N/m}$, pulled out $12\ \text{cm}$ and let go. You will make the program follow its energy over two swings and show that the total stays the same.

The idea. The block moves as $x = A\cos\omega t$, with $\omega = \sqrt{\dfrac{k}{m}}$, so its velocity is $v = -A\omega\sin\omega t$. Its energy is $U = \tfrac12 kx^2$ plus $K = \tfrac12 mv^2$.

Your tasks.

1. Work out $\omega$.
2. Work out U and K at every time in t.
3. Work out the total energy at every time, and its average.