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Unformatted text preview: an response would change with time. Thus, the steady-state response of a harmonic oscillator is at the driving frequency [omega] and not at the natural frequency [omega] . The general solution of the equation of motion is Substituting this expression into the equation of motion we obtain This equation can be rewritten by using some trigonometric relations This equation can only be satisfied if the coefficients of cos([omega]t) and sin([omega]t) are zero. This implies that and In general A != 0 and [omega] != [omega] . The first condition than shows that The second condition can now be rewritten as The amplitude of the harmonic oscillator is given by The amplitude of the oscillation of the system gets very large if [omega] approaches [omega] . The system is said to be in resonance when this happens....
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This document was uploaded on 11/25/2011.
- Fall '09