Determination of g using simple pendulum is a core Oscillations & Simple Harmonic Motion concept in Physics. This guide explains what it is, walks through a fully worked example, and lists the key equations you need — with a short quiz to test yourself.

Key equations and worked example

A simple pendulum has a string 1.0 m long (g = 9.81 m/s²). Period T = 2π·√(1.0/9.81) ≈ 2.01 s. Shorten the string to 0.25 m and T = 2π·√(0.25/9.81) ≈ 1.00 s — quartering the length halves the period. Releasing from 20° or 40° barely changes T (small-angle approximation).

• <code>Period T = 2π·√(L/g)</code>
• <code>Angular frequency ω = √(g/L)</code>
• <code>θ(t) = θ₀·cos(ωt) (small angles, θ from the downward vertical)</code>
• <code>Frequency f = 1/T = (1/2π)·√(g/L)</code>

Determination of g using simple pendulum in detail

Determination of g using simple pendulum is one of the central ideas in Oscillations &amp; Simple Harmonic Motion, and it appears in Physics curricula under Simple harmonic motion. It is worth learning deeply because it connects to so many other topics in this section.

A simple pendulum swings with simple harmonic motion for small angles: the restoring torque is proportional to the angular displacement. Remarkably, the period depends only on the string length and gravity — not on the bob&#39;s mass or (for small swings) the amplitude. This isochronism is why pendulums were used in the first accurate clocks, and measuring T lets you determine g.

For exams, the pattern is predictable: first a definition or statement of the result, then a direct numerical application of one of the equations above, then a "why" question — why the formula takes that form, or what changes when a variable is doubled or halved. The worked example and quiz below cover exactly that progression.

Quick self-check:

• Q: What happens to the period if the string length is doubled?<br />A: It increases by √2 (≈1.41×), because T ∝ √L.
• Q: Does a heavier bob swing faster?<br />A: No — mass cancels out; the period depends only on L and g.
• Q: Why does the pendulum hang straight down at rest?<br />A: That is the equilibrium position where gravity&#39;s torque about the pivot is zero; any displacement creates a restoring torque toward it.
• Q: How can a pendulum measure g?<br />A: Measure T for a known L, then g = 4π²L/T².