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? :)