# How does mass affect a pendulum's period?

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156
Jun 29, 2014

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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39
Apr 17, 2017

It does not affect the period of the pendulum.

#### Explanation:

The formula for period of pendulum is:
$T = 2 \pi \sqrt{\frac{l}{g}}$
where $T$ is the period, $l$ is the length of the string and g is the acceleration due to gravity.
$\therefore$ The mass does not affect the period of the pendulum.

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10
Sep 17, 2017

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

#### Explanation:

The formula
$T = 2 \cdot \pi \cdot \sqrt{\frac{l}{g}}$
assumes that all the mass is concentrated a distance $l$ from the pivot. In a clock's pendulum the bob is often a hanging chunk of lead. The rest of the pendulum is as light as possible so that the wire the bob hangs from can be ignored. This is the approximation I indicated in the "Answer" above. That assumption needs to be valid in the construction of the pendulum.

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 $l$ has decreased significantly. So the period would be much shorter.

I hope this helps,
Steve

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