# Question #6578f

Jan 28, 2017

For a simple pendulum making a small angle $\theta$ with the vertical we have its time period $T$, the time taken for a complete cycle as

$T = 2 \pi \sqrt{\frac{l}{g}}$
where $l$ is its length and $g$ is acceleration due to gravity.

Setting $T = \infty$, we get

Either $l = \infty$ or $g = 0$.
Physically it may not be possible to realize a pendulum with $l$ length as infinite.
However, there would arise situations where $g = 0$. Though division by $0$ is not defined we may be able to state that time period will be a very large undefined number.
it is same as running a pendulum in gravity free region,

Pendulum in a freely falling lift is an example of such a situation. In the frame of reference of lift we need to account for acceleration of so that so that Newton's Laws of motion are valid and could be applied. Hence, a pseudo force equal and opposite to downward force due to $g$ is added to acceleration of the lift.