## The Pendulum Problem

I was watching a film in my oceanography class about waves when I started to think about the energy loss and motion of pendulums. I want to know if a pendulum in a vacuum will ever stop moving completely. I know there is friction within the pendulum. I also know that the distance that the bob travels in each swing decreases multiplicatively. In calculus I learned that multiplying something by a number n such that 0<n<1 infinitely many times approaches 0. Does this apply to the pendulum's velocity?

Does a pendulum actually stop moving completely or does it seem to stop but still move?
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 Newton's first law states that unless an unbalanced force acts upon a body of matter, causing the mass to accelerate, the mass will stay at rest or travel indefinitely in a straight line with a constant velocity. Pendulums oscillate because gravity and the tension in the pendulum string/cable/ whatever are continuously acting upon the mass. Gravity still exists even in a vacuum. Even out in isolated space where gravity is less intrusive, if the pendulum were still magically swinging back and forth because of the presence of a magical force, the conservation of energy implies that some source of energy is being translated into the physical movement of the pendulum and that all of the energy will eventually become unusable heat.
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