A DSP text gives an example of an ideal mass striking an ideal string here:
This is drawn as an equivalent electrical circuit as follows, where each R represents one of the two string segments the mass interacts with (ie. the string segment to the left of the mass and the string segment to the right):
A piano hammer is imagined slightly differently as a mass driving a damped spring against the string here:
They state: "The impedance of this plucking system, as seen by the string, is the parallel combination of the mass impedance $ ms$ and the damped spring impedance $ \mu+k/s$. The damper $ \mu $ and spring $ k/s$ are formally in series."
I am wondering if anyone would be able to draw the equivalent electrical circuit for this interaction. I am trying to figure out how to write equations for the forces and velocities of a hammer modeled in this way but I think I need the diagram first.
This is my best guess. I put the damper and spring in series, and their combination in parallel to the mass which has the force exerted to it directly. I am uncertain of the + or - directions for the damper and spring:
Furthermore, in the first case of the mass striking a string, because all the elements were in series, I believe the sum of forces for the elements had to equal zero ($Fm(t) + Fr(t) + Fr(t) + Fext(t) = 0$). What would that equation of forces look like for this circuit?
I'm guessing it would be something like an equation system based on the parallel sections:
$Fm(t) + Fr(t) + Fr(t) + Fext(t) = 0$
$Fk(t) + Fr(t) + Fr(t) + Fext(t) = 0$
$Fm(t) = Fk(t)$
Is any of that right?