What happens mathematically to a pendulum if the length of the string is increased?
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It depends on the pendulum. In the case of simple, or mathematical, pendulum, the period does not depend on the mass. The simple pendulum is a small massive ball hanging on a long string (that is, the size of the ball is very small compared to the length of the string.) The period of such pendulum depends only on the length of the string and the gravitational acceleration:
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