Question:

Is the natural frequency of a pendulum affected by the mass of the pendulum?

Answer:

At first glance, one may be tempted to conclude that a larger mass must imply a larger inertia and thus lower acceleration, resulting in a longer period of oscillation.

In a pendulum, the restoring force is also proportional to the mass of the pendulum. (To be more accurate, both the restoring torque and the moment of inertia of a pendulum are proportional to the mass of the pendulum). So changing the mass does not change the acceleration of the pendulum. As a result, the natural frequency of a pendulum is not affected by its mass.

Does this remind you of how a heavier mass falls at the same rate as a ligher mass?

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