Period for Oddly Shaped Pendulums
Reference from the original Physics I textbook.
- Period for Oddly Shaped Pendulums
For small oscillations of a rigid physical pendulum, T ≈ 2π√(I/(mgh)), with scalar g and I about the pivot axis.
T = period (s); I = inertia about the pivot axis (kg·m²); m = mass (kg); g = gravitational-acceleration magnitude (m/s²); h = pivot-to-center-of-mass distance (m). The formula assumes small angular displacement.
- Related Glossary Terms
- Index
Reviewed physics notes (2)
These corrections keep the original lesson’s purpose while fixing errors in the source edition.
- Physical-pendulum formula needs pivot-axis I and small angles. — Reference 1
- Period requires scalar g and the small-angle approximation. — Reference 1
Glossary and deeper reading · 3 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Oscillation period
An oscillation period is the time required for one complete repeating cycle. It is the reciprocal of frequency and is measured in seconds. For example, measuring the time for several pendulum swings and dividing by the number of cycles estimates the period.
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Pendulum
A pendulum is a system that swings about a support under a restoring torque. A simple pendulum approximates a small mass on a light string and follows simple harmonic motion only for sufficiently small angles. For example, a short string pendulum completes small swings more quickly than a longer one under the same gravitational field.
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Simple harmonic motion
Simple harmonic motion occurs when the net restoring force is proportional to displacement from equilibrium and points in the opposite direction. The resulting position varies sinusoidally with time in the ideal model. For example, a mass attached to an ideal spring can execute simple harmonic motion when damping is negligible.