Question

current attempt in progress
five simple pendulums are shown in the drawings. the lengths of the pendulums are drawn to scale, and the masses are either m or 2m, as shown. which one has the smallest angular frequency of oscillation?

Explanation:

Step1: Recall the formula for angular frequency of a simple pendulum

The angular frequency \(\omega\) of a simple pendulum is given by \(\omega=\sqrt{\frac{g}{L}}\), where \(g\) is the acceleration due to gravity and \(L\) is the length of the pendulum. The mass of the pendulum bob does not affect the angular frequency.

Step2: Analyze the lengths of the pendulums

Since \(\omega\) is inversely proportional to \(\sqrt{L}\) (\(\omega\propto\frac{1}{\sqrt{L}}\)), the pendulum with the largest length \(L\) will have the smallest angular frequency.

Answer:

B