Calculate the period and frequency of a simple pendulum based on its length and the local acceleration due to gravity.
Last updated: March 2026 | By ForgeCalc Engineering
A simple pendulum is an idealized mathematical model of a pendulum. It consists of a point mass (the bob) suspended from a massless, inextensible string of length (L) that oscillates about a fixed pivot point under the influence of gravity.
The period of a simple pendulum is the time it takes to complete one full oscillation (back and forth). Remarkably, for small angles, the period depends only on the length of the string and the acceleration due to gravity, not on the mass of the bob or the amplitude of the swing.
Where:
• T is the period of the pendulum (s)
• L is the length of the string (m)
• g is the acceleration due to gravity (m/s²)
• π is approximately 3.14159
In the idealized simple pendulum model, the mass does not affect the period. This is because the gravitational force is proportional to the mass, which exactly cancels out the mass in the equation for acceleration.
It is 'simple' because it ignores air resistance, friction at the pivot, the mass of the string, and assumes the displacement angle is small (typically less than 15°).
The formula T = 2π√(L/g) is derived using the approximation sin(θ) ≈ θ. At larger angles, the period increases slightly and requires a more complex mathematical solution (elliptic integrals).
The period is inversely proportional to the square root of gravity. This means a pendulum will swing slower on the Moon (lower gravity) than on Earth.
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