## Abstract

Complex numbers play a very useful role in applied mathematics. As an example, let us consider the behavior of a particle of mass where or

*m*constrained to move in one dimension under the influence of an elastic force,$$F\, = \, - kx$$

*x*is the displacement of the particle from its equilibrium position and*k*is a constant. This relation is known as*Hooke’s law*. From Newton’s second law of motion (F =*ma*), we have$$- kx\, = \,m\frac{{d^2 x}}{{dt^2 }}\,$$

$$\,\frac{{d^{2x} }}{{dt^2 }}\, + \,\frac{k}{m}x\, = \,0.$$

## Keywords

Imaginary Part Complex Number Complex Variable Equilibrium Position Linear Differential Equation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer-Verlag New York, Inc. 2002