Read the notes, then try the practice. It adapts as you go.When you're ready.
Session Length
~17 min
Adaptive Checks
15 questions
Transfer Probes
8
Simple harmonic motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium and directed toward the equilibrium position: F = -kx. This relationship produces sinusoidal oscillations in time, characterized by amplitude, period, frequency, and phase. SHM is one of the most important models in physics because it describes a vast range of phenomena — from vibrating guitar strings to oscillating atoms in a crystal lattice to the behavior of AC electrical circuits.
The two canonical SHM systems are the mass-spring system and the simple pendulum (for small angles). For a mass on a spring, the period depends only on the mass and the spring constant: T = 2*pi*sqrt(m/k). For a simple pendulum, the period depends on the length and gravitational acceleration: T = 2*pi*sqrt(L/g). In both cases, the period is independent of the amplitude — a property called isochronism. The position, velocity, and acceleration of an SHM oscillator can be described by sinusoidal functions, and the energy continuously converts between kinetic and potential forms while the total mechanical energy remains constant.
AP Physics 1 requires students to analyze SHM quantitatively and qualitatively. Students must derive and apply period equations, describe the energy transformations during oscillation, interpret position-velocity-acceleration graphs, and connect SHM to circular motion. Extensions include damped oscillations (where energy is gradually lost to friction), driven oscillations (where an external periodic force sustains motion), and resonance (where the driving frequency matches the natural frequency, producing maximum amplitude). Understanding resonance is critical for engineering applications from bridge design to radio tuning.
One step at a time.
Adjust the controls and watch the concepts respond in real time.
Oscillatory motion where the restoring force is proportional to displacement from equilibrium: F = -kx. The motion is sinusoidal with constant amplitude, period, and frequency.
Example: A mass attached to a spring oscillates back and forth when displaced and released. The position as a function of time follows x(t) = A*cos(omega*t + phi).
The maximum displacement from the equilibrium position during oscillation. It determines the total energy of the system: E = (1/2)kA^2 for a spring system.
Example: If a pendulum swings 15 cm to either side of its rest position, its amplitude is 15 cm (0.15 m).
Period (T) is the time for one complete oscillation. Frequency (f) is the number of oscillations per second: f = 1/T. Angular frequency: omega = 2*pi*f = 2*pi/T.
Example: A pendulum that completes one full swing (back and forth) in 2 seconds has a period of 2 s and a frequency of 0.5 Hz.
A force that always points toward the equilibrium position and is proportional to displacement. For a spring: F = -kx (Hooke's Law). This force is what causes the oscillation.
Example: When you stretch a spring 10 cm beyond its natural length, it pulls back with a force proportional to that 10 cm stretch. Release it, and it oscillates.
A measure of a spring's stiffness, defined as the force per unit displacement: k = F/x. A stiffer spring has a larger k and produces a higher-frequency oscillation for the same mass.
Example: A spring with k = 200 N/m requires 20 N to stretch it 0.1 m. Attached to a 2 kg mass, it oscillates with period T = 2*pi*sqrt(2/200) = 0.63 s.
Total mechanical energy is constant and equals (1/2)kA^2. Energy oscillates between kinetic (max at equilibrium, KE = (1/2)mv^2) and potential (max at amplitude, PE = (1/2)kx^2). At any point: E = KE + PE.
Example: At the extreme position of a spring oscillator, all energy is potential (the mass is momentarily at rest). At equilibrium, all energy is kinetic (the mass moves fastest).
The phenomenon where the amplitude of a driven oscillation becomes maximum when the driving frequency equals the system's natural frequency. At resonance, energy transfer from the driver to the oscillator is most efficient.
Example: A child on a swing goes highest when pushed at the swing's natural frequency. Pushing at a different frequency produces smaller oscillations.
Oscillation in which the amplitude decreases over time due to energy loss from friction, air resistance, or other dissipative forces. The system eventually comes to rest at equilibrium.
Example: A car's suspension bounces a few times after hitting a bump, with each bounce smaller than the last due to shock absorbers (dampers) that dissipate energy.
More terms are available in the glossary.
Choose a different way to engage with this topic — no grading, just richer thinking.
Explore your way — choose one:
See how the key ideas connect. Nodes color in as you practice.
Walk through a solved problem step-by-step. Try predicting each step before revealing it.
This is guided practice, not just a quiz. Hints and pacing adjust in real time.
Small steps add up.
What you get while practicing:
The best way to know if you understand something: explain it in your own words.
More ways to strengthen what you just learned.