When does a pendulum bob move fastest and why?

A pendulum bob will move fastest when the mass is at its lowest point (when x=0). The reason for this is that in the pendulum system energy is transferred between kinetic and gravitational potential energy, and total energy will always be fixed in the system. Gravitational potential energy will be at its minimum when the bob is at the lowest point, meaning that kinetic energy will be at its maximum, resuting in the bob moving fastest at this point.