Period of a pendulum of infinite length?

Question

Consider a simple pendulum suspended from infinity (that is, very far from the Earth’s surface)
with the pendulum bob near the Earth’s surface. What’s the longest period of this pendulum? (Hint: you will need to explain why the period is longest when the amplitude is smallest).

za · Accepted Answer

If the pendulum were of infinite length the period would be infinite.

But the pendulum cannot have infinite length if it is to fit in this universe, so the period will be very large but finite.  Because information can only travel down the pendulum string at a maximum speed of light, so when you release the pendulum it will not move until a wave has travelled up to the point of suspension (distance = 13 billion light years) and back again, and that will take a minimum of the twice the age of the universe, some 25 billion years, and even then it will not have completed a cycle.  And in any case the universe will be twice as large then as it it now.

Hmmmm .....    You know, this question is more complicated than you might think.

Let&#39;slearntothink · Answer

One can take tangential to the earth's surface and then can prove that T = 2Ï*â(R/g), where R is the radius of he earth.

Piyush · Answer

after considering every aspect time period theoretically will be infinite

? · Answer

Hey, AP,

You  need  to  know   HOW  close  to  the  Earth's

surface....right ?  We'll be  waiting  for  the  info.  Also,

the  mass  in  grams  would  be nice.

Thanks !

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Period of a pendulum of infinite length?

4 Answers