Hooke's law and spring oscillation calculator
A spring stores energy as the square of its displacement, and oscillates at a rate set by stiffness over mass.
N/m
Restoring force
20N
- Stored energy
- 1
- Natural frequency
- 1.591 55 Hz
- Period
- 0.628 32 s
- Peak speed in oscillation
- 1
- Static sag under the mass
- 0.098 066 5
Show the working
- Spring constant = 200
- Displacement = 0.1
- Attached mass = 2
- Restoring force = 200 * 0.1 = 20
- Stored energy = 200 * 0.1^2 / 2 = 1
- omega = sqrt(200 / 2) = 10
- Period = 2 * pi / 10 = 0.628 319
- Natural frequency = 10 / (2 * pi) = 1.591 55
- Peak speed in oscillation = 10 * 0.1 = 1
- Static sag under the mass = 2 * g0 / 200 = 0.098 066 5
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- F = k x
- E = (1/2) k x^2
- omega = sqrt(k/m), T = 2 pi sqrt(m/k)