If two pendula have the same length but one has a 2 pound weight on its end while the other has only a 1 pound weight which will have the longer period

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Physics

Jaslyn Beck

4 August, 12:36

If two pendula have the same length but one has a 2 pound weight on its end while the other has only a 1 pound weight which will have the longer period

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Immanuel Patel · Answer 1

In calculations of the behavior of a pendulum, and in the formula that relates its period to its length, we always assume that it's swinging through "small angles", like less than 45 degrees.

Under this assumption, and the formulas we use every day for a pendulum, the mass doesn't matter. If you can rig one pendulum holding a little stone and another pendulum holding a school bus, and make them the same length, and eliminate air resistance, they'll both have the same period.

The Pendulum Period formula is:

Time = 2π · √ (length/gravity)

Mass is not even there in the formula. It makes no difference!