Pendulum Period
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For a simple pendulum, the period depends only on the length of the pendulum and the local acceleration due to gravity, following T = 2π√(L/g). Notably, it does not depend on the mass of the bob or, for small swings, the amplitude of the swing.

Both the gravitational force pulling the bob and its inertia (resistance to acceleration) scale with mass in exactly the same way, so mass cancels out of the equation entirely. A heavier bob feels more gravitational pull, but it also takes proportionally more force to accelerate, and the two effects offset perfectly.

Only slightly, and only if the swing is large. The standard formula assumes small-angle swings (under about 15-20 degrees), where the period is essentially constant regardless of amplitude; for wider swings, the true period becomes slightly longer than the formula predicts.

Period increases with the square root of length, so a pendulum four times as long takes twice as long to complete each swing. This relationship is why grandfather clocks with long pendulums tick at roughly one-second intervals, while a short desk pendulum swings much faster.

Because gravity varies slightly by location and altitude — it's marginally weaker at the equator and at high elevation, and marginally stronger toward the poles — the same pendulum will swing very slightly slower where gravity is weaker. This effect is small but was historically used to help measure variations in Earth's gravity.