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If we sit in the satellite's frame of reference(which is non-inertial because the satellite is accelerating) the pendulum's bob will feel a pseudo force just opposite to the gravitational force being applied on the bob, this will result into bob feeling no acceleration due to gravity which makes the time period infinite.

But how can we explain the time period being infinite from ground's frame(which is assumed to be not accelerating)?

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I am trying to give a non-mathematical but logical approach in my answer.


Consider the bob of the pendulum without any strings attached to it just above the ground. What will happen if you leave it?

It will fall.

Now suppose you attach the string at angle $\theta$ with the vertical. Then as soon as the bob is left -- Gravity will try to pull it down but the string will intervene and cause the bob to swing in an oscillatory motion.


Now consider the bob without any strings attached to it in a space craft orbiting the Earth. What will happen if you leave it?

Nothing.It will not fall down (with respect to the space craft). It is already in a state of free fall.

In such a case, why will attaching a string to it make it go about in an oscillation. After all the reason for Tension in the string in the Earth case was to prevent the bob from falling. Here it is not falling (with respect to the space craft) anyway.

Get it?

Now we call its Time Period infinite as it is never able to complete its oscillation. How could it - the oscillation never even started!


P.S.

  1. I am assuming that you know the basics of free fall and gravity. For any queries, comment below.

  2. Note that all my observations are from ground frame.

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