Pendulum - Calculate Length, Time, Amplitude and Angle

Calculator for a simple mathematical pendulum. This is an ideal cord pendulum with negligible friction and cord mass, which is swinging in a small angle. The weight is concentrated on one point. Then the pendulum law, which was discovered by Galileo Galilei, says that the oscillation period only depends on its length. The formula is t = 2 π √ l / g . This formula provides good values for angles up to α ≤ 5°. The larger the angle, the more inaccurate this estimation will become. From the angle, the amplitude can be calculated and from amplitude and oscillation period finally the speed at the pendulum's center can be calculated. A single oscillation begins and ends at the same state of motion, so an oscillation has the length 4a. A mathematical pendulum would swing forever, a real one is slowed down by friction. The amplitude will get lower, the oscillation period stays constant until the pendulum halts.

Please enter length or oscillation period, the other value will be calculated. When angle, amplitude or speed are entered, the other two values also will be calculated.

Example: a 2 meters long pendulum has an oscillation period of 2.8 seconds. At an angle of 5°, the amplitude is 17.5 centimeters and the speed is 0.9 km/h.

The Foucault pendulum in the Deutsches Museum in Munich consists of a 30 kilogram lead ball on a 60 meter long wire rope. The large mass ensures that the pendulum swings for a long time before it has to be pushed again. The length gives the pendulum a swing period of about 15 1/2 seconds. With an amplitude of three meters, it has a speed of 2.78 kilometers per hour and an angle of 2.865 degrees.

Length l:
Oscillation period t:		seconds
Gravitational acceleration g:		m/s²

Angle α:		degrees
Amplitude a:
Speed v:
Round to decimal places.