SIMIODE resources are here. Use the Browse menu to find Modeling Scenarios and Resources migrated from the old website.



Modeling Scenario


Author(s): John Thoo

Keywords: oscillation Archimedes’ Principle buoancy oscillatory motion Newton's Second Law

49 total view(s), 9 download(s)


Resource Image In this scenario, we lead students through the process of building a mathematical model for a floating rectangular box that is bobbing up and down.


Researchers should cite this work as follows:

Article Context

Resource Type
Differential Equation Type
Qualitative Analysis
Application Area
Lesson Length
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Bloom's Cognitive Level


The principal forces acting on the box are its weight (the force due to gravity) and the buoyancy force (that makes it float). By Archimedes' Principle, the buoyancy force acting on an object equals the weight of the liquid that is displaced by the object.

If an object that is in water is in equilibrium (neither sinking nor rising), then the buoyancy force that is acting on the object is equal in magnitude and in the opposite direction to the force due to the weight of the object. If the object is submerged below its equilibrium (floating) position, then the buoyancy force will cause the object to rise. The upward motion would move the object above its equilibrium position, and then the weight of the object would cause it to fall. The downward motion would move the object below its equilibrium position, and then the buoyancy force would cause the object to rise again, and the cycle would repeat indefinitely (bobbing up and down) if there were no friction (damping, drag).

Activity 1

The goal is to come up with a mathematical model for a floating rectangular box that bobs up and down in water.

Activity 2

Suppose that the box described above develops a leak in its bottom, and that water is flowing into the box.

Activity 3

In Activity 1, we assumed that the box is floating in still water, and that the only forces that are acting on the box are its weight and the buoyancy. We now add the assumption that a third force, friction or drag, is also acting on the box.

Activity 4

The box is held with its bottom 0.8 m below the surface and then released from rest.

Article Files


Author(s): John Thoo



There are no comments on this resource.