Симулятор пружины-массы
Параметры #1
Уравнение движения
m·x" + c·x' + k·x = 0
ω₀ = √(k/m) = 3.162 rad/s
ζ = c / (2√(mk)) = 0.079
ω_d = ω₀√(1-ζ²) = 3.152 rad/s
The units behind this oscillation
A spring–mass system is set by three quantities, and its rhythm follows from two of them. Follow any into the converter, or see how the units themselves are built from the SI base units.
What you are changing
The same 1 kg mass on five different springs
| Spring constant k | Natural frequency f | Period T |
|---|---|---|
| 5 N/m | 0.356 Hz | 2.81 s |
| 20 N/m | 0.712 Hz | 1.40 s |
| 50 N/m | 1.125 Hz | 0.89 s |
| 200 N/m | 2.251 Hz | 0.44 s |
| 500 N/m | 3.559 Hz | 0.28 s |
Calculated live from ω₀ = √(k/m) with m = 1 kg (no damping), using the same function the simulation integrates with. Stiffen the spring 100× and the rhythm only speeds up 10× — frequency goes as √k.
Why the mass cancels in a pendulum but not here
A pendulum's period is 2π√(L/g) — no mass in it. A spring's is 2π√(m/k) — mass right in the middle. The difference is where the restoring force comes from: gravity pulls harder on heavier things (so mass cancels), while a spring pulls with the same k no matter what you hang on it. Same-looking formula, opposite behaviour.
How the SI units are defined →