Brian said:

Though it is quite possible to use several different physical pairs

for C and L anologs, I confirm that for mass and springs,

Bill is spelling out a pairing that I know is in use: i.e. the spring

is not the L as you might suppose, but the C.

Brian Whatcott Altus OK

For a mass-spring system, if we assume a rectifying force which is

dependent on position, then

F = -k*x

By newtons famous law,

F = m * a

So, if x is a function of time, we have

-k*x(t) = m * x''(t)

thus,

x''(t) = -k/m * x(t)

The solution is, of course,

x(t) = sin(sqrt(k/m) * t)

where sqrt(k/m) is called the 'angular frequency'

For electronics, if we say that

k = 1/C, and m = L, then

v(t) = sin(t/sqrt(LC))

This makes the resonant frequency w = 1/sqrt(LC), which we know to be

the case.

By this, we can say that the spring is the equivalent to the capacitor,

and the mass is equivalent to the inductor.

Another way to look at it is that the fundamental correpondence is mass

and charge. The spring creates a rectifying force, just like the voltage

across the capacitor induces the charges to move. Once the mass is in

motion, its inertia keeps it going, which is what F = ma is all about.

An inductor opposes motion, and then wants to keep the motion going,

just like inertia.

Thus, the real correspondence is voltage across the capacitor to tension

in the spring, and the movement of charge throught the inductor to the

inertia of the mass.

For more information, you can consult "The Feynman Lectures", volume I,

chapter 23. He uses a cool technique to derive the equations of damped

oscillation for both mass-spring and inductor-capacitor systems.

--

Regards,

Robert Monsen

"Your Highness, I have no need of this hypothesis."

- Pierre Laplace (1749-1827), to Napoleon,

on why his works on celestial mechanics make no mention of God.