In the and directions respectively. Dividing the top equation by the bottom gives

Next, since we will only discuss small oscillations (larger oscillations are still harmonic, but are not simple), we will approximate the tangent by sine (remember this procedure - it is often used). Thus we have

where is the length of the pendulum. So if we compare this equations with the spring equations from before we see that we have

From this expression we can find as

To find the maximum kinetic energy we will use the velocity if we
remember an equation from circular motion:

so that

and finally