Question

Describe the relationship between the length and period of a pendulum in the language of direct proportions

Answer 1

The period of the pendulum is directly proportional to the square root of the length of the pendulum

Explanation:

The period of a simple pendulum is given by the equation

$T=2\pi \sqrt{\frac{L}{g}}$

where

T is the period

L is the length of the pendulum

g is the acceleration of gravity

From the equation, we see that when the length of the pendulum increases, the period of the pendulum increases as the square root of L, $T\propto \sqrt{L}$. This means that

The period of the pendulum is directly proportional to the square root of the length of the pendulum

From the equation, we also notice that the period of a pendulum does not depend on its mass.

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