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Infinite length Simple Pendulum

What is the time period of a simple pendulum of infinite length.

The answer is 86 minutes.

Can anyone explain this?

Note by Selena Miller
2 years, 11 months ago

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t = 2 * pi * sqrt( l / g )

so i think if the its length is infinite so the time period also will be infinite :D

i don't know whether i am right or wrong :D Sherif Elmaghraby · 2 years, 11 months ago

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Time period of a long pendulum is given by \(\frac { 2\pi }{ \sqrt { \left( \frac { 1 }{ R } +\frac { 1 }{ l } \right) g } } \)
for infinite pendulum 1/l will be neglected and the formula will be \(2\pi \sqrt { \frac { R }{ g } }\)
which on solving results in 86 mins Rohit Gupta · 1 year, 8 months ago

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You should consider a pendulum with the length L which is much longer than the Earth radius R. If you then use for the description of the pendulum motion the conservation law in the gravitational field (not in the uniform field), you will get the following result - angular frequency to the second power will be equal to g/R. Сергей Кротов · 2 years, 11 months ago

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@Сергей Кротов You are right, it is just the change of g in the points close to the surface that makes the system oscilate harmonically. You should consider the change of the gravitational energy when the displacement is small and equate it to the change of kinetic energy. Finally in this particular case when the body is close to the surface of the Earth (in the strong limit L>>R) the period wouldn't depend on L. Сергей Кротов · 2 years, 11 months ago

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it is because t=2pisqrtradius of earth/g Varun Khare · 2 years, 11 months ago

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Can someone please post a detailed proof?? Amlan Mishra · 10 months, 1 week ago

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THE LENGTH OF THE PENDULUM IS MUCH LONGER THAN THE RADIUS OF THE EARTH SO IN THE FORMULA OF THE TIME PERIOD WE CONSIDER THE CHANGE IN THE VALUE OF g. Pranjal Rajawat · 2 years, 11 months ago

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