Which one of the following statements regarding a simple pendulum is correct? Simple pendulum has a time period independent of amplitude:
only for small amplitudes because then the net force on its bob is independent of its displacement.
for any amplitude because the net force on the bob is always proportional to its displacement.
for any amplitude because the net force on the bob is independent of its displacement.
only for small amplitudes because then the net force on its bob is proportional to its displacement.
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC NDA-1 – 2024
The motion of a simple pendulum is approximately Simple Harmonic Motion (SHM) for small angular displacements (amplitudes). In SHM, the restoring force is directly proportional to the displacement from equilibrium (and directed towards equilibrium). For a simple pendulum, the restoring torque (or force component) is proportional to sin(theta), where theta is the angular displacement. For small theta, sin(theta) โ theta (in radians), which means the restoring force is proportional to the angular displacement and, consequently, the arc displacement. This proportionality is the condition for the period to be independent of amplitude.