How is the period of a pendulum dependent on the length and mass of the pendulum?
The time period of a simple pendulum is given as per the following equation:
`T = 2pi sqrt(L/g)`
where T is the time period, L is the length of the pendulum and g is acceleration due to gravity.
Two things are clear from this equation:
1) The mass of the pendulum has no effect on the time period of the pendulum, since mass is absent from this equation. Thus, we can use a small and light pendulum or a large and heavy pendulum and our time period will stay the same, as long as the length of the pendulum is constant.
2) Time period is dependent on the length of the pendulum, L. The time period varies as square root of L. Thus, if you change the length of the pendulum by a factor of 4, the time period doubles. Or, if reduce the pendulum length to 1/4 its original value, the time period halves.
Thus, T`!=` f(m) and T = f(L)
Hope this helps.
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