# How does mass affect a pendulum's period?

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The mass of a pendulum's bob does not affect the period.

Newton's second law can be used to explain this phenomenon. In F = m a, force is directly proportional to mass. As mass increases, so does the force on the pendulum, but acceleration remains the same. (It is due to the effect of gravity.) Because acceleration remains the same, so does the time over which the acceleration occurs.

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It does not affect the period of the pendulum.

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The formula for period of pendulum is:

where

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Within certain limits, mass does not affect a pendulum's period.

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The formula

assumes that all the mass is concentrated a distance

If you increase the mass of the bob, that is no problem since it makes the above assumption more valid (mass is even more concentrated at the end). When you write in your comment about "mass is removed", are you referring to removing the bob entirely? If you do that (or substitute a much lighter bob), you would have to consider that

I hope this helps,

Steve

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