Multiple Representations is the idea that a physical phenomena can be explored in many different ways. For example, there is the physical representation which models the system with figures and diagrams, such as a free body diagram. There is also the mathematical representation which uses the equation(s) governing the physics of the system. All of the representations can be used together to help us understand and quantify the physical phenomena.

 

Observe the different types of representations for this section below;

Physical Representations explain the features of the situation in a visual way, often with vector representations of physical quantities overlaid a simple diagram or picture of the situation.

A coupled system of masses.

Mathematical Representation uses equation(s) to describe the situation.

An example problem walking through Newton's second law for a coupled system

Graphical Representation describes the situation through use of plots and graphs.

A plot of the displacement of the two coupled objects shown in the image below. Notice that the constraint is ▲x2=½▲x1

                                     

 
Descriptive Representation is made up enitrely of words or annotations. Think about how you might explain the situation to someone else.

 Box A is sitting on a table. It is connected to box B by a massless string. I slid box A along the table at a constant 5 m/s. Since box A and box B are connected box B will also move at 5 m/s. Also, as the string is massless the force of tension from the string on each box will be the same.

Actual Phenomena could be thought of as doing the experiment. For example, if you're asked which of two runners, with different characteristics of their speeds, will win the race, one way to determine that would be to get two runners to run in the described way and see who wins.

A video of the Atwood Machine. This is just two nearly equal masses connected over a near-frictionless pully.