Abstract
We examine an experimental apparatus that is used to motivate the connections between the basic properties of vectors, potential functions, systems of nonlinear equations, and Newton's method for nonlinear systems of equations. The apparatus is an adaptation of a force table where we remove the center-pin and allow the center-ring to move freely. The new apparatus can be used in both static and dynamic modes. If the vector forces are not balanced, the center-ring moves freely around the table, until it comes to rest under the influence of friction from the pulleys. The determination of the equilibrium point is a non-trivial exercise in vector addition and systems of non-linear equations. The dynamic situation also motivates the study of systems of nonlinear differential equations.
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