Simple Harmonic Motion (Spring–Mass) Calculator
Calculates period, frequency and the x–v–a time table of simple harmonic motion from spring constant, mass and amplitude.
Info
Simple harmonic motion (SHM) occurs when the restoring force acting on an object displaced from equilibrium is proportional to the displacement. The spring–mass system is the most classic example of this motion. Key relationships: - Hooke's Law: F = −k·x - Equation of motion: m·x'' + k·x = 0 - Angular frequency: ω = √(k/m) - Period: T = 2π / ω - Frequency: f = 1 / T - Displacement: x(t) = A·cos(ωt + φ) - Velocity: v(t) = −A·ω·sin(ωt + φ) - Acceleration: a(t) = −A·ω²·cos(ωt + φ) For given m, k and A this tool: - Finds the period, frequency and angular frequency, - Calculates maximum velocity and acceleration, - Generates an x(t), v(t), a(t) table at the selected time step.
- Spring–mass systems at small amplitudes are good models of simple harmonic motion.
- Under the small-angle assumption, pendulum motion can also be treated as approximately SHM.
- In SHM energy continuously exchanges between potential and kinetic forms; total mechanical energy is constant.
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