QuestionJuly 28, 2025

Essay: In your own words, explain why a simple pendulum's period does not depend on the mass on the end of the pendulum. square

Essay: In your own words, explain why a simple pendulum's period does not depend on the mass on the end of the pendulum. square
Essay: In your own words, explain why a simple pendulum's period does not depend on the mass on the end
of the pendulum.
square

Solution
4.5(224 votes)

Answer

The period of a simple pendulum does not depend on the mass because mass cancels out in the equations of motion, leaving the period dependent only on the length of the pendulum and gravitational acceleration. Explanation 1. Identify the formula for the period of a simple pendulum The period T of a simple pendulum is given by **T = 2\pi \sqrt{\frac{L}{g}}**, where L is the length of the pendulum and g is the acceleration due to gravity. 2. Analyze the formula components Notice that the formula does not include mass (m). It only depends on L and g. 3. Understand the physics behind the formula The restoring force in a pendulum is gravitational, which is proportional to mass. However, mass also appears in inertia (resistance to motion), canceling out its effect on the period.

Explanation

1. Identify the formula for the period of a simple pendulum<br /> The period $T$ of a simple pendulum is given by **$T = 2\pi \sqrt{\frac{L}{g}}$**, where $L$ is the length of the pendulum and $g$ is the acceleration due to gravity.<br /><br />2. Analyze the formula components<br /> Notice that the formula does not include mass ($m$). It only depends on $L$ and $g$.<br /><br />3. Understand the physics behind the formula<br /> The restoring force in a pendulum is gravitational, which is proportional to mass. However, mass also appears in inertia (resistance to motion), canceling out its effect on the period.
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