Here we return to the simple (or mathematical) pendulum which we also considered in the first lecture. Then we figured that the amplitude of the pendulum motion does not figure into the period of oscillation. This time we will worry about the amplitude not because we are going to revise our opinion on its irrelevance to the pendulum period but because we want to exercise our formulae and save our daring volunteer. I need someone with nerves of steel and blind faith in the physics professor. A person stands at the point of release of bowling ball pendulum. If that person remains in place the pendulum will return to the exact same location.
Analysis: In this experiment we started with a certain amount of potential
energy. and no kinetic energy. Choosing floor level as the point of
zero potential energy and assuming that nose-height is 
m
then
Since only gravity does work in this problem mechanical energy must be conserved
and hence upon return the highest the pendulum can go will correspond to the
point at which its kinetic energy has vanished and then
Applying the law of conservation of mechanical energy we have
We can use the same law of mechanical energy conservation in the absence of dissipation to derive the speed at the low point in the trajectory. For that we
obviously choose the low point as the ``final state'' where
Equating the initial and final mechanical energies we obtain
Here we see how the choice of zero for potential energy
never has significance in properties which we can actually measure.
The expression for the max velocity only contains the height difference
and leaves no trace of the fact that we chose the zero for potential energy
as floor height.