---------------------------------------------------------------------
Hi all,
Three questions related to the LC circuit/mass-spring analogy...
1) According to Halliday, Resnick, and Walker's "Fundamentals of
Physics" (Fourth Edition) the analogy between elements and variables in an
LC circuit and a mass/spring system goes like this...
LC <--> M-S
-----------
q <--> x
i <--> v
C <--> 1/k
L <--> m
My first question is, "What is the mechanical analogy of potential
difference?" (This is actually a question in the book.) I feel that I
have the answer they are looking for, but I was wondering what other people
would come up with.
2) My next question is how does one present the answer to the above
question in a light that may not be confusing to the students?
3) What are some limitations of the LC <--> M-S analogy?
Thanks in advance for any insights you may have on these questions.
--------------------------------------------------------------------------------
My response:
I presume we are talking about the potential difference across the capacitor.
Then V=q/C and application of the analogous relationships gives the analogous
quantity as kx, which we recognize as the (time dependent) force of the spring
on the mass.
I share your frustration in dealing with the student response to presentation
of analogies like this. Students seem to view them as lacking rigor. "Sure, I
can see how that *might* be the case, but *maybe* if you did the problem over
from scratch you would find a different answer." I see this tied up with the
investment students have in always using the same symbols for given quantities.
They really have yet to see that mathematics is divorced from the meaning of
the symbols and the physical quantities can be given any symbol we like.
This is further evidencd by the fact that students often don't recognize that
the equations they have seen in math are the same as they are seeing in
physics, just with different symbols.
I guess what I try to do is keep the two analogous fundamental equations on the
board along with the analogous solutions and talk about how the manipulations
that you would do to solve the problem *have* to be the same, only the symbols
change. They acknowledge it intellectually, but you can tell that there is
substantial remaining skepticism.
I don't see too many limitations to the analogy. The only thing I can think of
is that nonlinearities enter into each system in different ways.