AP Physics 1 · Unit 7 · Oscillations

Pendulums Practice Problems

Use swing timing, gravity, and energy to explain pendulums and compare them with spring oscillators.

12 questions6 conceptual · 6 calculation

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Simulation scene from the Pendulums lesson. — A scene from the related lesson. Open the practice to work through the questions.

What you’ll practice

Connect swing timing with forces and energy

Find period, length, and local gravity

Use the small-angle pendulum model to estimate a tower height, choose lengths for different worlds, or infer gravity from timed full oscillations. Keep pivot-to-center length distinct from floor clearance.

Explain the lowest point of a swing

Calculate speed from gravitational energy, separate zero tangential acceleration from nonzero inward acceleration, and use the radial force balance to find string tension.

Compare pendulums with spring systems

Predict the effects of changing mass, length, release angle, and gravity. Contrast gravity-dependent pendulum timing with spring timing and account for energy in a cord-and-spring comparison.

A question from this set

Does a heavier bob swing more slowly?

Two ideal simple pendulums have the same pivot-to-bob-center length and the same small release angle. One bob has four times the mass of the other. How do their periods compare?

Their periods are equal.
The heavier bob has twice the period.
The heavier bob has four times the period.

Try it in the practice set

Compare two bob masses at the same pivot-to-center length and small release angle.

Key ideas

Know which approximation and acceleration you are using

Small-angle timing has a limited range

The familiar pendulum period assumes a small release angle. A larger-angle swing takes longer at the same length; inserting that period into the small-angle inverse formula overestimates the length. A different bob mass does not explain the shift.

A bottom crossing still requires inward acceleration

The tangential component of gravity vanishes at the lowest point, but the bob is moving along a curved path. Tension exceeds weight so their difference provides the inward force needed to change the velocity direction.

See the physics

Measure real crossings and compare energy stores

After attempting the questions, run native string-and-bob swings under the stated gravity. Record full periods between same-direction crossings or pause at the first bottom crossing to inspect force and acceleration. The worksheet’s spring comparisons use actual attached springs, a cord, and a fixed pulley.

Use a hint for a starting point or open a worked solution to follow the reasoning. Your progress saves in this browser, so you can return to unfinished questions.

Ready for pendulums?

Begin with a conceptual question, then work through the calculations.

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