Examples of differential equations: Difference between revisions

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where ''m'' is the mass and ''k'' is the spring constant that represents a measure of spring stiffness. For simplicity's sake, let us take ''m=k'' as an example.

If we look for solutions that have the form <math>Ce^{\lambda t}</math>, where ''C'' is a constant, we discover the relationship <math>\lambda^2+1=0</math>, and thus <math>\lambda</math> must be one of the [[complex number]]s <math>i</math> or <math>-i</math>. Thus, using [[Euler's theoremformula]] we can say that the solution must be of the form:

: <math>x(t) = A \cos t + B \sin t</math>