Approximate analytical solution to oscillations of a conductor in a magnetic field
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An approximate analytical solution to a system exhibiting oscillations of a conductor in a magnetic field which is controlled by a discrete waveform is sought by means of multiple scales. The system involves the use of a solenoid driven by a RLC circuit, coupled with a solid state relay (SSRL), to generate large electromagnetic forces acting on a conductor, which oscillates within the solenoid. The steady state response of the metal bar, in terms of oscillations is described. This solution is expressed in terms of system and circuit parameters, valid in the weakly nonlinear region, which is identified to be small oscillatory displacement near the center of the solenoid. By analyzing different cases of resonance, period-1 and period-2 like motions are identified and validated through experimental studies. The solution provides a guideline to design an effective control strategy so as to guide the system to a desirable attractor.
KeywordsOscillations Approximate analytical method Multiple scales Magnetic field Conductor
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