Circuit/Mechanical oscillator analogy

[jdstokes]

Homework Statement

I've been pondering the analogy between an RLC circuit and a damped harmonic oscillator.

The inductor serves the role of the inertia, leading a finite charging frequency.

What happens if we remove the inductor, so that the system consists just of a charged capacitor, with each plate connected by a wire of resistance R?

The Attempt at a Solution

The mathematics suggests that the system will undergo oscillations with an effectively infinite frequency and that the amplitude will instantly decay to zero.

This doesn't seem to make sense. What would really happen?

 

[jdstokes]

For anyone interested, my initial guess is rubbish: with no inductor, there is no interchange between energy stored by the magnetic and electric fields, so the charged capacitor simply discharges exponentially to zero.

 

[thomate1]

I would like to address the question of what would really happen if we removed the inductor from the RLC circuit analogy. First, it is important to understand the purpose of the inductor in the circuit and its role in creating oscillations. The inductor stores energy in its magnetic field and resists changes in current, leading to the characteristic frequency and damping in the circuit.

If we were to remove the inductor, the system would no longer have a means to store energy and resist changes in current. This would result in a lack of oscillations and the current would simply flow through the circuit without any changes or decay. In other words, the system would behave more like a simple resistor-capacitor circuit.

However, this does not necessarily mean that the amplitude would instantly decay to zero. There may still be some small fluctuations in the current due to the capacitor's ability to store energy. The exact behavior of the system would depend on the specific values of resistance and capacitance in the circuit.

In summary, removing the inductor from the RLC circuit would result in a different behavior of the system, but it is not accurate to say that the amplitude would instantly decay to zero. It is important to consider the role of each component in the circuit and how their removal would affect the overall behavior.