A simple pendulum is a small mass (the bob) hanging from a string of fixed length that swings back and forth under gravity; for small angles it undergoes simple harmonic motion with period T = 2π√(L/g), which depends only on the string's length and the gravitational field, not the bob's mass.
A simple pendulum is the most stripped-down oscillator you'll meet in AP Physics 1. Take a small sphere, hang it from a string with negligible mass, fix the top end, and pull the bob to the side. Gravity does the rest. The component of gravity along the arc acts as a restoring force, always pulling the bob back toward the lowest point (the equilibrium position). For small angles, that restoring force is proportional to displacement, which is the defining condition for simple harmonic motion.
The payoff is the period equation T = 2π√(L/g). Read it carefully, because what's missing matters as much as what's there. The period depends on the length of the string and the acceleration due to gravity, and that's it. A heavier bob doesn't swing slower, and a slightly bigger amplitude doesn't change the timing (as long as the angle stays small). You can also think of the pendulum as a rotating system, since the bob sweeps an arc about the fixed pivot. That's why it lives in Unit 6 alongside rotational kinetic energy, where K = ½Iω² describes the energy of anything spinning about an axis.
The simple pendulum anchors Topic 6.1, Period of Simple Harmonic Oscillators, in Unit 6 (Energy and Momentum of Rotating Systems). It connects to learning objective 6.1.A because a pendulum is a rigid system rotating about a fixed pivot, so its kinetic energy can be written as rotational kinetic energy, K = ½Iω². For an object rotating about a fixed axis, that rotational kinetic energy is the object's total kinetic energy. The pendulum is also the exam's favorite vehicle for testing whether you understand SHM at the conceptual level. Can you identify the restoring force? Can you predict what happens to the period if length doubles or if the pendulum moves to the Moon? Can you track energy as it shifts between gravitational potential energy and kinetic energy through a swing? Those are exactly the moves AP Physics 1 questions ask for.
Keep studying AP Physics 1 Unit 6
Restoring Force (Unit 6)
A simple pendulum only oscillates because gravity has a component along the arc that always points back toward equilibrium. That's the restoring force, and recognizing it on a free-body diagram is the first step in almost every pendulum problem.
Acceleration due to gravity (Unit 2)
Since T = 2π√(L/g), the pendulum's period is a direct probe of the local gravitational field. Same pendulum on the Moon, where g is smaller, swings with a longer period. This is a classic AP question setup, and it works because g sits in the denominator.
Equilibrium position (Unit 6)
The bob's lowest point is where the net tangential force is zero and speed is maximum. Velocity peaks at equilibrium while acceleration peaks at the endpoints of the swing, which is exactly backwards from what intuition suggests and exactly what MCQs love to test.
Rotational Motion (Units 5-6)
A pendulum is really a mass rotating about a fixed pivot, so you can describe it with angular velocity and rotational kinetic energy, K = ½Iω². That framing is why the simple pendulum shows up in Unit 6 with the other rotating systems.
The simple pendulum shows up in both multiple-choice and free-response questions, and the 2024 exam's Short FRQ Q4 used one directly. That question hung a small sphere from a string with negligible mass and pulled it to a small angle θ, which is the standard setup. Notice the language, because it matters. "Negligible mass" string and "small angle" are the exam's signals that the simple pendulum model and T = 2π√(L/g) are valid. Expect to do three things with this term. First, reason proportionally about the period (quadruple the length and the period doubles, since T goes as √L). Second, explain in writing why mass and small changes in amplitude don't affect the period. Third, track energy through the swing, with gravitational potential energy at the endpoints converting to kinetic energy at the bottom. MCQs often ask where speed, acceleration, or net force is greatest during the swing, so know the equilibrium point versus the turning points cold.
Both undergo simple harmonic motion, but their periods depend on different things. The pendulum's period, T = 2π√(L/g), depends on length and gravity but NOT mass. The mass-spring system's period, T = 2π√(m/k), depends on mass and spring constant but NOT gravity (a horizontal spring oscillator works the same on the Moon). If an exam question moves an oscillator to another planet, the pendulum's period changes and the spring's doesn't. Mixing up which formula ignores mass is one of the most common point-losers in this unit.
A simple pendulum is a bob on a string of negligible mass swinging under gravity, and for small angles it undergoes simple harmonic motion.
Its period is T = 2π√(L/g), so it depends only on string length and gravitational field strength, never on the bob's mass.
Quadrupling the length doubles the period, and moving the pendulum to a location with weaker gravity (like the Moon) makes the period longer.
The restoring force is the component of gravity along the arc, and it always points toward the equilibrium position at the bottom of the swing.
Speed and kinetic energy are maximum at the equilibrium position, while acceleration and restoring force are maximum at the endpoints of the swing.
Because the bob rotates about a fixed pivot, the pendulum's kinetic energy can be written as rotational kinetic energy, K = ½Iω², tying it to the rest of Unit 6.
It's a small mass (bob) hanging from a string of negligible mass and fixed length that swings under gravity. For small angles it's a simple harmonic oscillator with period T = 2π√(L/g), covered in Topic 6.1.
No. Mass cancels out of the equation of motion, so the period T = 2π√(L/g) doesn't include mass at all. A bowling ball and a golf ball on identical strings swing with the same period, and explaining why is a classic AP question.
Both are simple harmonic oscillators, but the pendulum's period depends on length and gravity (T = 2π√(L/g)) while the spring's depends on mass and spring constant (T = 2π√(m/k)). On another planet, the pendulum's period changes and the spring's stays the same.
The period increases by a factor of √2, about 1.41 times longer, because period scales with the square root of length. To double the period you'd need to quadruple the length.
Yes. The 2024 exam's Short FRQ Q4 used a sphere on a negligible-mass string pulled to a small angle θ, and pendulum questions regularly appear in multiple choice testing proportional reasoning with T = 2π√(L/g) and energy conservation through a swing.