Simple Harmonic Motion (SHM) simulator

Q: Which equations does the SHM simulator use?

It derives omega = sqrt(k/m) to report period T = 2pi/omega, applies x(t) = A cos(omega t + phi), v(t) = -A omega sin(...), a(t) = -omega^2 x(t), and logs energy with K = 0.5 m v^2 and U = 0.5 k x^2.

Q: When should I choose Euler-Cromer or RK4?

Euler-Cromer is quick and energy-stable for coarse time steps, while RK4 tracks the analytic curve to within 1e-3 for the same grid; both methods export the same table and How it's calculated log.

Spring-mass parameters

Mass m (kg)

Spring constant k (N/m)

Initial condition mode

Amplitude A (m)

Phase phi (deg)

Method

t max (s)

Time step dt (s)

Evaluation time t* (s)

Keyboard shortcuts: Ctrl+Enter runs the solver, Ctrl+S downloads the CSV.

Result summary

How it's calculated

Time series and energy

Inspect displacement, velocity, acceleration, and energies at each time step. The plot overlays displacement x(t) with total energy E(t).

t (s)	x (m)	v (m/s)	a (m/s^2)	K (J)	U (J)	E (J)

FAQ

Which equations does the SHM simulator use?

The solver computes omega = sqrt(k/m) for the spring-mass system, reports the period T = 2pi/omega, and evaluates x(t), v(t), a(t), and the energy terms K = 0.5 m v^2 and U = 0.5 k x^2. The analytic, Euler-Cromer, and RK4 solvers all log their steps in the How it's calculated list.

When should I choose Euler-Cromer or RK4?

Euler-Cromer is fast and keeps energy bounded for larger time steps, making it useful for exploratory lessons. RK4 is higher order and matches the analytic curve to within the required 1e-3 tolerance while still emitting the same time series table and CSV export.

Result summary

How it's calculated

FAQ

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