A pendulum is an object suspended from a fixed pivot that swings back and forth along an arc because gravity acts as a restoring force; for small angles it behaves as a simple harmonic oscillator with period T = 2π√(L/g), which depends on length and g but not on mass or amplitude.
A pendulum is a mass (the bob) hanging from a fixed point that swings freely under gravity. Pull it to one side and the component of gravity along the arc pulls it back toward the lowest point, its equilibrium position. It overshoots, swings up the other side, and repeats. That back-and-forth motion is periodic, and for small angles it's simple harmonic motion (SHM).
The 'simple pendulum' on the AP exam means a small sphere on a string of negligible mass. Its period is T = 2π√(L/g). Read that equation carefully, because it's where the exam questions live. Period depends on the string's length and on g, the local acceleration due to gravity. It does NOT depend on the bob's mass or (for small angles) the amplitude of the swing. The small-angle condition matters because the restoring force is only approximately proportional to displacement when θ is small, and that proportionality is what makes motion count as SHM.
The pendulum lives in Topic 6.1, Period of Simple Harmonic Oscillators (Unit 6). It's one of the two classic oscillators you must know, alongside the spring-block system. If the pendulum is a swinging rigid object rather than a bob on a string, its kinetic energy is rotational, K = ½Iω², which is exactly what learning objective AP Physics 1 Revised 6.1.A asks you to describe.
It also doubles as a go-to setup for energy conservation in Topic 4.3. As the bob swings down, gravitational potential energy converts to kinetic energy, and the speed at the bottom comes straight from energy conservation, not kinematics. That two-for-one is why pendulums keep showing up on FRQs. One apparatus tests both your oscillation reasoning and your energy reasoning.
Keep studying AP Physics 1 Unit 6
Period of Simple Harmonic Oscillators (Unit 6)
The pendulum is the gravity-powered version of SHM. Compare T = 2π√(L/g) with the spring formula T = 2π√(m/k). Length plays the role mass plays for a spring, and g plays the role of k. Knowing which variable matters for which oscillator is a classic MCQ trap.
Conservation of Energy (Unit 4)
A swinging pendulum is energy conservation drawn as an arc. Height above the lowest point stores gravitational PE, the bottom of the swing is all KE, and the total stays constant if you ignore air resistance. Use mgh = ½mv² to find the speed at the bottom from the release height.
Acceleration due to gravity (Unit 1/2)
Because T = 2π√(L/g), a pendulum is literally a g-measuring device. A lab-style question can give you period and length data and ask you to extract g from the slope of a T² vs. L graph. On the Moon, where g is smaller, the same pendulum swings slower.
Damping and Air Resistance (Unit 6)
A real pendulum doesn't swing forever. Air resistance does negative work each cycle, so the amplitude shrinks while mechanical energy leaves the system. The interesting twist is that for small angles the period barely changes even as the swing dies down.
Pendulums show up in both multiple choice and free response. The 2024 Short FRQ Q4 is the template, a small sphere hanging from a string of negligible mass, pulled to a point so the string makes a small angle θ, then released. From there you might be asked to compare periods after changing length, mass, or amplitude, sketch energy bar charts at different points in the swing, find the speed at the bottom using energy conservation, or explain in words why mass doesn't appear in the period. The phrase 'small angle' in the stem is doing real work. It's the signal that SHM equations apply. For paragraph-length responses, the winning move is to connect the equation to the physics, for example arguing that doubling the mass doubles both the restoring force and the inertia, so the period is unchanged.
Both are simple harmonic oscillators, but their periods depend on different things. A spring-block system has T = 2π√(m/k), so mass matters and gravity doesn't (a horizontal spring oscillates the same on the Moon). A pendulum has T = 2π√(L/g), so mass doesn't matter but gravity does. If an exam question moves an oscillator to another planet or swaps the mass, ask yourself which formula governs it before answering.
A simple pendulum's period is T = 2π√(L/g), so it depends only on string length and the local value of g.
The bob's mass does not affect the period, because a heavier bob feels a proportionally larger restoring force and has proportionally more inertia.
Pendulum motion only counts as simple harmonic motion for small angles, which is why FRQ stems specify that the string makes a small angle θ.
A swinging pendulum trades gravitational potential energy for kinetic energy, so you find its speed at the bottom with energy conservation, not kinematics.
A longer pendulum swings with a longer period, and a pendulum on the Moon (smaller g) swings slower than the same one on Earth.
Air resistance damps a real pendulum, shrinking its amplitude over time, but for small angles the period stays essentially the same.
It's a mass hanging from a fixed pivot that swings back and forth under gravity. For small angles it's a simple harmonic oscillator with period T = 2π√(L/g), covered in Topic 6.1.
Neither. The period T = 2π√(L/g) has no mass in it, so doubling the bob's mass leaves the period unchanged. Extra mass means more restoring force but also more inertia, and the two effects cancel exactly.
Both oscillate in SHM, but a spring's period (T = 2π√(m/k)) depends on mass and not gravity, while a pendulum's period (T = 2π√(L/g)) depends on gravity and not mass. Taking each to the Moon gives opposite results, the spring is unchanged and the pendulum slows down.
SHM requires the restoring force to be proportional to displacement. Gravity's restoring component on a pendulum is only approximately proportional to displacement when the angle is small, which is why exam problems, like the 2024 Short FRQ Q4, always specify a small angle θ.
Yes. The 2024 exam included a Short FRQ built around a simple pendulum released from a small angle, and multiple-choice questions regularly test what changes the period (length and g) versus what doesn't (mass and small amplitude).