Can a pendulum vibrate in an artificial satellite?

OR: What will be the time period of a simple pendulum in an artificial satellite?

OR: Can a pendulum clock be used in an artificial satellite?

The time period of a simple pendulum is, \[T=2π\sqrt{\frac{l}{g}}\]

In an artificial satellite, the effective value of acceleration due to gravity $g$ is zero. \[\therefore T=2π\sqrt{\frac{l}{g}}=2π\sqrt{\frac{l}{0}}=\infty\]

This means that a pendulum cannot vibrate in an artificial satellite.

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