Help determining the equivalent mechanical system for a filter?

[achilles03]

I'm a little rusty on my circuit analysis, so I was hoping someone more well-versed in circuit analysis could give me a little help in figuring out a filter I'm interested in. I believe it is a Butterworth filter.

I'm a mechanical engineer, and it'd be easier to set up the differential equation if I could visualize it mechanically. So, if anyone could help, what would the equivalent mechanical system be for the following filter?

http://www.wenzel.com/graphics/pinet.gif

I think that it's a dashpot and spring in parallel with a mass (I hope this pastes ok):

----------
---DASHPOT----| |
| mass |
----SPRING------| |
----------

...but I can't figure out where to place the left-most capacitor. Is in in series with the dashpot?

The end result is that I want to model the transient response (using a step-time type integration) for non-linear voltage inputs (square, saw, etc).

Thanks in advance for any help!
Dave

 

[achilles03]

It looks like I was incorrect in calling it a Butterworth filter. It looks like this is a pi filter.

 

[PHovnanian]

                           +-----+
                       Fv1 |     |  Fv2
     (fixed) o--@@@@@---+--|  M  |--+---@@@@@@---o (fixed)
                 Kc1       |     |  |    Kc2
                 spring    +-----+  |  spring   -+
                                    |           ||
                                    +-----------||----o (fixed)
                                                ||
                                                -+
                                              dashpot


         Where: electrical param                mechanical param
         -----------------------                ----------------
         V1 (voltage)                           Fv1 (force)
         V2 (voltage)                           Fv2 (force)
         Il (inductor current)                  Vm  (mass velocity)
         Qc1 (charge on C1)                     Xc1 (spring displacement)
         Qc2 (charge on C2)                     Xc2 (spring displacement)        
To apply V1, apply a force to point Fv1. To measure V2, measure the force
between the mass and Fv2.

 

[achilles03]

Fantastic, thanks! I wrote a quick-check in Excel, and the math works out. Is this the response you'd expect for a square wave input close to the resonant frequency?

Thanks again,
Dave

 

[IRstuff]

Unless you do a Bode plot, there's no way to tell, other than that it's a low pass filter, given the series L and R.

However, the pi filter cited has 4 passive components, while the mechanical "equivalent" only has 3.

TTFN

FAQ731-376

 

[achilles03]

1 mass, 2 springs, 1 dashpot... that's 4 passive components.