analogues
analogues
The circuit where R, L, and C elements are arranged as a filter section, a Laplace transform is written and solved for steady state and transient frequency response.
The analogue in mechanics is a spring and shock absorber mechanical suspension system. The RLC electronic filter and the mechanical analogue, spring + shock absorber, elements can be arranged so that the differential equation and the Laplace transform are identical mathematically in every way. Given only the equation one cannot distinguish if the origin was an electronic or mechanical system. The algorithm for solving and results are identical.
Rather than visualizing the purpose of reactance in the circuit, look at its perfect analogue, the spring shock absorber.
You're in the truck and drive over railroad tracks at 35 mph, perpendicular to the tracks. What happens.
The tire hits the first track and is driven up into the suspension, the spring compresses and the shock absorber builds pressure in the reservoir. The impact is "filtered" by the suspension, you feel the bump but don't break your back from it.
The tire has an instant when upward travel is max and upward velocity is zero. The tire begins the down stroke. On the upstroke the suspension received energy, received movement (displacement), and stored it. Now on the down stroke there is air under the tire, the tire moves down, powered mostly by the stored energy from the suspension system.
That is one half of the sine wave, up and down over the rail. If the tire fell into a hole, immediately after the upward impact of the rail, that would be the second half of the sinewave as the tire falls into the hole and is driven back out.
Note that at any instant we could look at our recording equipment and know instantaneous F=Kx, force on the spring due to displacement, shock absorber reservoir pressure. However the instantaneous values do not contain essential information. We do not know if the tire is traveling up or down, how fast it is moving, and we do not know the forcing function, the road ahead, is it another rail, a hole, or a turnpike. Isolated instantaneous values only convey the static case. The suspension could be compressed but not moving, or if moving, how fast? We need to know the instantaneous di/dt, dv/dt , rate of change, frequency of the input. Given frequency of the input and the constants for L, C, the output frequency response can be calculated.