A pendulum is a simple device composed of a weight suspended on a string, wire, metal or other material that swings back and forth. Pendulums have been used in grandfather clocks and the like to keep time. Scientific principles govern what affects the swing rate of the pendulum. These principles predict how a pendulum behaves based upon its features.
TL;DR (Too Long; Didn't Read)
The forces of gravity, the mass of the pendulum, length of the arm, friction and air resistance all affect the swing rate.
Pull a pendulum back and release it. You can let the pendulum swing back and forth on its own, or in the case of a clock, have it swing powered by the gears. Either way the principle of periodic motion affects the pendulum. The force of gravity pulls the weight, or bob, down as it swings. The pendulum acts like a falling body, moving toward the center of motion at a steady rate and then returning.
The swing rate, or frequency, of the pendulum is determined by its length. The longer the pendulum, whether it is a string, metal rod or wire, the slower the pendulum swings. Conversely the shorter the pendulum the faster the swing rate. This represents an absolute principle that will always work no matter the type of design. On grandfather clocks with long pendulums or clocks with shorter ones, the swing rate depends upon the pendulum's length.
Amplitude refers to the angle of swing, or how far back the pendulum swings. A resting pendulum has an angle of 0 degrees; pull it back halfway between resting and parallel to the ground and you have a 45-degree angle. Start a pendulum and you determine the amplitude. Experiment with different starting points and you discover that the amplitude does not affect the swing rate. It will take the pendulum the same amount of time to return to its starting point. One exception involves a very large angle, one beyond any reasonable swing for a clock or any other device. In that case the swing rate will be affected as the pendulum goes faster.
One factor that does not affect swing rate is the weight of the bob. Increase the weight on the pendulum and gravity just pulls harder, evening out the extra weight. As School for Champions points out, the force of gravity on any falling object is the same no matter what the object's mass.
In a real-world application air resistance affects the swing rate. Each swing encounters that resistance and it slows down the swing, although it might not be enough to be noticeable during one swing. Friction also slows down the swing. If the pendulum is swinging based upon inertia from the initial release eventually it will come to a stop.
The swing rate of a pendulum adjusts when placed in close proximity to another pendulum. This phenomenon is called sympathetic vibration. The pendulums pass motion and energy back and forth. This transfer will eventually cause the swing rate of one pendulum to be identical with that of the other pendulum.