Simulate spring-mass simple harmonic motion with analytic, Euler-Cromer, or RK4 solvers. Follow each step in How it's calculated and export charts, tables, and CSV files.
Built for physics and calculus lessons. Derive amplitude and phase from x₀ and v₀, keep omega and energy summaries visible, and share the same setup by URL. Calculations stay in your browser.
Default spring-mass sample: m = 1.0 kg, k = 4.0 N/m, A = 0.1 m.
Angular frequency ω = 2.00 rad/s, period T = 3.14 s, frequency f = 0.318 Hz.
We model a one-dimensional spring-mass system. The tool computes ω = sqrt(k/m) and T = 2π/ω, then evaluates x(t), v(t), and a(t) from the SHM equations. It also logs kinetic, potential, and total energy over time.
Euler-Cromer is simple and keeps energy reasonably bounded, even with larger time steps. It works well for quick classroom demos. RK4 is higher-order and usually tracks the analytic curve within about 1e-3, so it suits accurate plots and assignment checks.
All calculations run in your browser only. The inputs you enter are not sent to the server, so you can safely use classroom examples or assignment data.
Use mass, spring constant, amplitude, and phase first. For the default sample, m = 1.0 kg and k = 4.0 N/m give ω = 2.00 rad/s, so you can check the period before changing the solver method.
The analytic method uses the closed-form SHM equations. Euler-Cromer and RK4 depend on the time step, so reduce dt when you need the numeric curve to match the analytic baseline more closely.
Use this page to connect period, frequency, angular frequency, amplitude, mass, and spring constant for ideal simple harmonic motion. Start with the known physical quantities and the model type.
Keep SI units consistent unless the page explicitly converts them. Mass-spring and pendulum assumptions are different, so do not transfer values between models without checking formulas.
A useful sequence is to compute the base period or frequency, then vary one physical parameter to see whether the motion changes as expected.
Do not treat this as a damping or driven-oscillation model. Friction, large angles, and external forcing require a different setup.
Read the direction of change as a model check: increasing spring stiffness should shorten the period, while increasing mass should lengthen it in the mass-spring case.