Simple pendulum
A mass on a string swinging through small angles. Its period T = 2 pi sqrt(L/g) depends on length, not mass.
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Analogy
A playground swing with a longer chain swings slower.
Example
T = 2 pi sqrt(L / g)T = 2 pi sqrt(1 / 9.8)T = 2.01 s
In practice
A 1.00 m pendulum swings once every 2.0 s on Earth.
Practice
Flashcards
- Does a pendulum's period depend on its mass?No. It depends on length and g only.
Interview questions
- A pendulum clock runs slow on a mountain top. Explain why.
- Period depends on g
- g is slightly smaller at altitude
- Smaller g gives longer period
Questions people ask
Why does the pendulum formula only work for small angles?
For small angles, the restoring force is nearly proportional to the angle, which gives SHM. At large angles the force grows more slowly, so the period increases. Below about 10 degrees the formula is accurate to within about 0.2 percent, which is fine for exams.
How can a pendulum measure g?
Time many swings of a pendulum of known length, find the period T, then rearrange T = 2 pi sqrt(L/g) to get g = 4 pi squared L over T squared. A 1.00 m pendulum with a 2.01 s period gives g of about 9.77 m/s squared.