Pendulum period: √length, not mass

Quadruple a pendulum’s length and it swings half as fast. Mass doesn’t matter at all.

Why it works

T ∝ √L, and mass cancels out of the equation entirely — same reason heavy and light objects fall together.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

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More in Physics Simulation

• ζ = 1 is critical dampingWhen the damping ratio hits 1, the system returns to rest as fast as possible without overshoot …
• A metre swings in two secondsA 1 m pendulum takes almost exactly 2 s per full swing.
• Falling: 5 metres in the first secondA dropped object falls ~5 m in the first second and gains ~10 m/s of speed every second.
• 45° for range — in a vacuumWithout air drag, 45° maximizes projectile range; with drag, the real optimum is nearer 30–40°.

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