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# Infinite length Simple Pendulum

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

Can anyone explain this?

Note by Selena Miller
3 years, 5 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 · 3 years, 5 months ago

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 · 2 years, 2 months ago

bhai,how did you get this formula,proof?? · 6 months, 1 week ago

What is R? Also, what if the pendulum is in a gravity free region? Won't the friction of pendulum parts slow it down? Will the time period be different for the types of material we use to make bob and the pendulum?

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. · 3 years, 5 months ago

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. · 3 years, 5 months ago

it is because t=2pisqrtradius of earth/g · 3 years, 5 months ago

Ans is 84.6 minute · 5 months, 1 week ago

Can someone please post a detailed proof?? · 1 year, 4 months ago