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Oscillation of a floating body
Intermediate
A buoyant object bobbing in liquid is SHM.
A floating cylinder displaced vertically by y feels a restoring force −ρAgy, so it performs SHM with T = 2π√(m/ρAg).
A cork bobbing in water.
Neglects water motion and drag.
In more detail
A floating body that is displaced vertically oscillates about its equilibrium because buoyancy provides a restoring force. Its period depends on its shape, mass and the density of the fluid.
Real-world uses
- Buoys and ships oscillate when disturbed by waves.
- Engineers design floating platforms to avoid resonance with waves.
- A buoy bobbing on the sea, or a ship rolling in waves, oscillates about its floating equilibrium.
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Frequently asked questions
What is the restoring force?
The change in buoyancy as the body moves up or down.
Does the body's shape matter?
Yes. The waterplane area affects the stiffness and therefore the period.
What is the restoring force for a floating body?
The buoyant force, which increases when the body is pushed deeper and decreases when it rises.
Related topics in Oscillations & SHM
Nonlinear oscillators · Chaos and the double pendulum · Parametric resonance · Liquid in a U-tube · Tunnel through the Earth · Molecular vibrations