Pendulum
A simple pendulum oscillates in the vertical plane due to gravity. Calculate the oscillating period or length of a pendulum using the fundamental pendulum equation.
Simple Pendulum Calculator
A simple (mathematical) pendulum consists of a rigid body suspended from a fixed horizontal axis about which the body oscillates in a vertical plane due to gravity.
Formula:
T = 2π√(l/ag)
Where:
- T = oscillating period for one cycle (s)
- l = length of the pendulum (m)
- ag = acceleration of gravity (9.81 m/s²)
Rearranged to solve for length:
l = (T/(2π))² × ag
Examples
Pendulum Clock (1 second period):
- l = ((1)/(2π))² × 9.81 = 0.249 m
- Pendulum clocks were the world standard for accurate timekeeping for 270 years until the quartz clock was invented in 1927.
Longer Period (10 seconds):
- l = ((10)/(2π))² × 9.81 = 24.9 m
Very Long Period (100 seconds):
- l = ((100)/(2π))² × 9.81 = 2487 m
Types of Pendulums
- Compound or Physical Pendulum - A rigid body suspended from a fixed horizontal axis
- Simple or Mathematical Pendulum - Mass concentrated in a single point, connected by a weightless chord
- Conical Pendulum - Weight moves in uniform speed around a circle in the horizontal plane
- Torsional Pendulum - A disk fixed to a slender rod that oscillates about the rod's axis