Velocity
Calculating the velocity of the pendulum bob at the equilibrium position requires that we arrange
our coordinate system so that the height of the bob at the equilibrium position is zero. Then the
total mechanical energy is equal to the kinetic energy at the equilibrium point where U = 0. The
total mechanical energy is also equal to the total potential energy at where KE = 0. Putting
these equalities together, we get
But what is h?
From the figure, we see that. If we plug that value into the equation above,
we can solve for v: