Simple pendulum
Also called Pendulum
A simple pendulum is a point mass hanging from a light string of fixed length, swinging under gravity. Displaced by a small angle it moves in simple harmonic motion with a period set only by the string length and g.
AP Physics C: Mechanics EK 7.5.A.3 defines it as a special case of a physical pendulum in which the hanging object can be modeled as a point mass a distance from the pivot. The period is
which is printed on all four AP Physics equation sheets. With , a 1.0 m pendulum has s.
Two things it does not depend on. Mass, because cancels: the same gravitational force that restores the bob also resists its acceleration. And amplitude, by EK 7.3.A.2.
The small-angle condition is part of the formula, not a footnote. AP Physics 1 EK 7.2.A.1.ii gives for a pendulum displaced by a small angle, and EK 7.1.A.2.iii says a pendulum's motion can be modeled as simple harmonic motion because the restoring torque is proportional to the angular displacement, which only holds for small displacements. C: Mechanics writes the approximation out as (EK 7.5.A.2.ii). Swing the bob through 60 degrees and the true period runs longer than the formula returns.
Note the in the formula: a pendulum clock keeps different time on the Moon, while a mass on a spring does not care.
Worked pendulum problems live in the SHM guide and the SHM practice set.