What a pendulum's period depends on
T = 2π√(L/g) — length and gravity matter, mass doesn't.
Appears onAP Physics 1
The common mistake
Thinking a heavier bob swings slower or faster. For a simple pendulum, mass doesn't appear in the period at all.
Instead: Use T = 2π√(L/g) for small swings. Only the length and g change the period. A mass on a spring is different: T = 2π√(m/k), where mass does matter.
Worked example with Guide me
A pendulum's length is made 4 times longer. What happens to its period?
- Sugar · How does T depend on L?Student · T is proportional to √L.
- Sugar · What's √4?Student · 2.
- Sugar · So what happens to T?Student · It doubles.
Answer: The period doubles. Changing the mass would change nothing.
Try 3 practice questions
1. The bob's mass is doubled. What happens to the period?
2. The length is cut to one quarter. What happens to the period?
3. Does a mass on a spring's period depend on mass?
Quick answers
- What is the most common mistake with what a pendulum's period depends on?
- Thinking a heavier bob swings slower or faster. For a simple pendulum, mass doesn't appear in the period at all.
- How do I get what a pendulum's period depends on right?
- Use T = 2π√(L/g) for small swings. Only the length and g change the period. A mass on a spring is different: T = 2π√(m/k), where mass does matter.
- Can you show a worked example?
- A pendulum's length is made 4 times longer. What happens to its period? The period doubles. Changing the mass would change nothing.
Related concepts
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