Infinite acceleration of bob in pendulum with no friction or air resistance

Question

So i'm a bit confused about something. If we take a mathematical pendulum and we apply a force to it. We ignore all friction and air resistance and only consider gravity and the force applied to bob. My question is and what i've figured out so far: If the force applied to the bob is less than the acceleration due to gravity, the bob will have a forever constant period of swings. However, if the force applied to the bob is greater than the acceleration due to gravity - does that mean that the bob will accelerate infinitely? Or does it only mean that the bob will have an infinite swing in one direction? I can't figure out if the acceleration will decay due to gravity when the initial force applied to the bob is greater than the acceleration due to gravity.

Anyone who care to help? :)

S Bateman · Answer

Whenever a pendulum moves, it accelerates since the velocity vector is constantly changing. So any pendulum that 'pendulates' forever will 'accelerate' forever. However, I think the acceleration you are talking about is better described as angular acceleration. Perhaps a better way to describe it is if it will complete a full rotation with increasing frequency. The answer to that question is no. The pendulum will have a constant oscillation frequency because the gravity that accelerates it on the way down is exactly equal to the gravity that decelerates it on the way up.

Answered by S Bateman on December 12, 2021

Infinite acceleration of bob in pendulum with no friction or air resistance

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