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Vertical spring
Intermediate
Gravity only shifts the equilibrium, not the period.
springGravity only shifts the equilibrium by mg/k; oscillations about that new point have the same period 2π√(m/k).
m = 1 kg, k = 100 N/m: sag 9.8 cm, T = 0.63 s.
Measure x from the new equilibrium.
In more detail
A vertical spring oscillates about a new equilibrium, shifted by the weight. The period is the same as for a horizontal spring, because gravity only shifts the equilibrium point.
Real-world uses
- Bungee cords and vertical springs in machines oscillate in this way.
- Ball and spring toys bounce vertically at a fixed period.
- A bungee cord or a hanging mass bobs with the same period as a horizontal spring, with gravity only moving the equilibrium point.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Does gravity change the period?
No. It only shifts the equilibrium position.
How far does the equilibrium move?
By mg divided by k, the static extension of the spring.
Does gravity change the period of a vertical spring?
No. It shifts the equilibrium position, but the period is set by the mass and stiffness alone.
Related topics in Oscillations & SHM
Phase difference · Phasor representation · Mass–spring system · Springs in series/parallel oscillations · Simple pendulum · Small-angle approximation