Question

What affects the swing rate of a pendulum?

Answer 1

Factors affecting the swing rate of a pendulum

Motion

1. Release a pendulum by pulling it back. The pendulum can be allowed to swing back and forth on its own or, in the case of a clock, it can be made to swing by the movement of the gears.
2. The pendulum is impacted by the periodic motion concept either way. As the weight swings, or bobs, gravity pulls it downward. The pendulum behaves like a body falling, steadily heading toward the center of motion, then swinging back.

Length

1. The length of the pendulum affects its frequency or swing rate. Whether it be a string, metal rod, or wire, a pendulum swings more slowly the longer it is.
2. It can be mathematically expressed as $f=\frac{1}{2\pi }\sqrt{\frac{g}{L}}$, where $f$ is the swing rate, $g$ is the acceleration due to gravity and $L$ is the length of the string of pendulum.
3. On the other hand, the swing rate increases with pendulum length. This is an example of an unchanging principle that applies to all kinds of designs.
4. The swing rate varies depending on the length of the pendulum on grandfather clocks, whether they have long or short ones.

Amplitude

1. The angle of swing, or how far back the pendulum swings, is referred to as amplitude. A pendulum at rest has an angle of 0 degrees; when it is pulled back halfway between rest and parallel to the ground, it has an angle of 45 degrees.
2. You may measure the amplitude by starting a pendulum. When experimenting with various beginning positions, you find that the swing rate is unaffected by the amplitude. The pendulum will swing back to its starting position in exactly the same period of time.
3. A very big angle that is outside the range of a clock's or any other device's realistic swing constitutes one exception. In that situation, when the pendulum swings quicker, the swing rate will be impacted.

Mass

1. The weight of the bob is one element that has no bearing on the swing rate.
2. The frequency is given by the formula $f=\frac{1}{2\pi }\sqrt{\frac{mgh}{I}}$, where $m$ is the mass, $g$ is acceleration due to gravity, $h$ is height of the pendulum and $I$ is moment of inertia.
3. Gravity will simply pull harder to balance off the increased weight as the pendulum's weight increases. No matter the mass of an object falling, the force of gravity acting on it is the same, as School for Champions points out.

Air resistance/Friction

1. In a practical setting, air resistance influences the swing rate. Although it might not be enough to be felt during one swing, each swing faces that resistance, which slows the swing down, $swingrate\propto \frac{1}{airresis\tan ce}$.
2. The swing is also slowed down by friction. The pendulum will eventually come to a stop if it is swinging due to inertia from the original release, $swingrate\propto \frac{1}{friction}$.