Oscillations and Resonance
Resonance occurs in any oscillatory
system when the frequency of the driving force is near the natural frequency of the
system. At the resonant frequency of a linear system the amplitude of oscillation is
at its maximum value. Therefore, in a linear system of oscillation there is a direct
correspondence between the amplitude of oscillation and the driving frequency, and thus a
periodic input always results in a periodic output. However, a non-linear system may
oscillate at various amplitudes for one particular driving frequency because the elements
of the driving force may not vary linearly with the space parameters. Therefore,
there is no unique maximum resonant amplitude in a non-linear oscillatory system and a
periodic input may not result in a periodic output. In such a non-linear oscillatory
system one may observe chaotic behavior in the output of the system. This paper
examines normal resonance in a linear oscillatory system within the study of vibrating
plates, a Helium-Neon Laser and a Carbon Dioxide Laser. It then explores resonance
in a non-linear oscillatory system, which may result in chaotic behavior, within the study
of a pendulum and an RLC circuit.
Table of Contents:
Discussion of Oscillation and Resonance in Linear and
Oscillations and Resonance in Linear Systems
- Vibrating Plates
- Helium-Neon Laser
- Carbon Dioxide Laser
Oscillations and Resonance in Non-Linear Systems
- RLC Circuit
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