To determine the number of natural frequencies of a pendulum, we consider the nature of the pendulum’s motion.
For a simple pendulum, the system consists of a mass (or bob) attached to the end of a lightweight cord that swings back and forth. Assuming that the displacements are small, the motion of a simple pendulum can be approximated by simple harmonic motion (SHM). Simple harmonic motion is characterized by oscillations where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.
Under this approximation, a simple pendulum exhibits:
1. A single mode of motion, which is the back and forth swinging.
This mode of motion corresponds to a single frequency at which the pendulum naturally oscillates. This frequency is determined based on factors such as the length of the pendulum and the acceleration due to gravity.
Therefore, a simple pendulum under SHM has one natural frequency of oscillation.
So the answer is:
One
