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Potential energy is the energy of a body or a system due to the position of the body or the arrangement of the particles of the system.

4 votes

Gravitational potential energy at $r = \infty$

I'm +1 on the answer by @ohneVal, but to add a different perspective, I think part of your conceptual problem is reflected by writing "$r=\infty$", whereas the rigorous statements are of the form "$r …
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3 votes
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If I have a simple pendulum performing oscillations, whose string is snapped when it is at a...

At the extreme position (max height), the mass on the end is momentarily at rest. If the string breaks at that moment, you just have a mass in the air acted on only by gravity. It will drop straight …
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