Question

Imagine a simple pendulum swinging in an elevator. If the cable holding the elevator up was to snap, allowing the elevator to go into free fall, what would happen to the frequency of oscillation of the pendulum? Justify your answer.

Answer 1

One of the components that affect the period is gravity (the other is length). This gravity is basically the value of the effective acceleration that acts on the body due to gravity. When the elevator is over free fall, the effective gravity becomes zero. Mathematically this can be visualized as,

$T = 2\pi \sqrt{\frac{l}{\dot{g_{eff}}}}$

Since this value is zero, the period would tend to be infinite,

$T \rightarrow \infty$

Therefore the frequency that is inversely proportional to the period would be defined as

$f = \frac{1}{T}$

$f = \frac{1}{\infty}$

$f \approx 0$

In this way there is no frequency on the body which will not generate any oscillation on the body