Simple Pendulum Calculator
Calculate the period and frequency of a simple pendulum.
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Enter the length of the pendulum in meters. The calculator computes the period and frequency using g = 9.81 m/s2, assuming small oscillation angles.
About Simple Pendulum
The simple pendulum is a classic system in physics. Its period depends only on the length of the string and the local gravitational acceleration: T = 2 pi sqrt(L/g). This result, valid for small angles, was studied by Galileo and later refined by Huygens and Newton. Pendulums have been used in clocks, seismometers, and gravity measurements. The simple pendulum demonstrates that the period of oscillation is independent of mass and amplitude (for small swings).
Frequently Asked Questions
What affects the period of a pendulum?
For a simple pendulum, only the length and gravitational acceleration affect the period. Mass and amplitude (for small angles) do not matter.
Why does mass not affect the period?
A heavier pendulum has more gravitational force but also more inertia. These effects cancel exactly, so the period depends only on length and gravity.
When does the simple pendulum formula break down?
The formula T = 2 pi sqrt(L/g) is accurate only for small angles (less than about 15 degrees). At larger angles, the period increases and the full elliptic integral solution is needed.