Question 1

What is the period of a simple pendulum?

Accepted Answer

The period T = 2π√(L/g), where L is the length in meters and g is gravity (9.81 m/s²). The period depends only on length and gravity — not on mass or (small) swing amplitude.

Question 2

How long should a pendulum be for a 1-second period?

Accepted Answer

For a 1-second period on Earth, L = g × (T/2π)² = 9.81 × (1/6.283)² ≈ 0.248 m, about 25 cm. A 1-meter pendulum swings with a period of about 2.0 seconds.

Question 3

Does the mass of the bob affect the period?

Accepted Answer

No. For a simple pendulum the period depends only on length and gravity, not on the bob's mass. A heavier and lighter bob at the same length swing in sync (assuming small angles).

Question 4

What is the small-angle approximation?

Accepted Answer

The formula T = 2π√(L/g) is accurate for swing angles under about 15°. At larger angles the true period grows slightly longer; this calculator uses the standard small-angle model used in physics classes.