A Simple Laboratory Experiment on Coupled Electrical Oscillators

The resonance properties of coupled LRC electrical oscillators was investigated and their joint behaviour compared to that of a mechanical mass-spring system.The damped sinusoidal output of each uncoupled circuit was recorded and curve fitting was performed to obtain values for the frequency and damping coefficients.Accurate values for the circuit resistance and inductance were calculated based on these parameters and the measured capacitance of the circuit.The circuits were then coupled with a capacitor, allowing energy to flow between them.The resultant output was recorded for each circuit and the resonance properties were observed.Energy was exchanged between the two circuits, resulting in a beating pattern where the amplitudes of each are fully out of phase.The "beat frequency" of the coupled LRC circuits was found to be f beat = 173.0 0.4 Hz.Coupling capacitance between the circuits was computed with significant accuracy; C coupling = 4.1 0.2 nF as compared to the measured 4.13 0.10 nF.Results from this experiment are compared to the mechanical mass-spring system, in which a mass is suspended from a spring and allowed to move freely, exhibiting initial vertical movement upon being pulled down and released, which then translates to horizontal movement over time.The momentum of the mass will oscillate between horizontal and vertical until it stops moving, similar to how the energy of the LRC circuit oscillates between capacitors after each pulse.The combined total momentum/energy outputs of both setups exhibit a similar damped sinusoidal oscillation, and energy of the mass-spring system is exchanged between planes of motion similarly to the coupled capacitor system.A beating pattern can be observed in the amplitudes of both oscillations in this system.The equations of motion describing the spring pendulum system are compared to the results of the coupled LRC system, demonstrating that these systems are mathematically equivalent.