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[[image:ScottHamiltonspring.jpg]] | [[image:ScottHamiltonspring.jpg]] | ||
| − | The natural frequency of oscillation for this system is computed as <math> \omega_0 ^2 = \frac{S}{m} </math> | + | The natural frequency of oscillation for this system is computed as <math> \omega_0 ^2 = \frac{S}{m} </math>. |
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| + | The behavior of this spring-mass system can then be modeled using complex numbers. | ||
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| + | Displacement | ||
| + | |||
| + | <math> x=A_1*e^{j * \omega_0 * t} + A_2*e^{-j * \omega_0 * t} | ||
Revision as of 16:26, 4 September 2008
Complex numbers can be used to represent waves and calculate their behavior. The simplest example of complex waves would be a simple mass, m, attached to a spring of stiffness S.
The natural frequency of oscillation for this system is computed as $ \omega_0 ^2 = \frac{S}{m} $.
The behavior of this spring-mass system can then be modeled using complex numbers.
Displacement
$ x=A_1*e^{j * \omega_0 * t} + A_2*e^{-j * \omega_0 * t} $
