Re: [Phys-L] overdamping

[John Denker <jsd@av8n.com>]

On 10/21/2015 01:20 PM, Carl Mungan wrote:
> * but the one that puzzles me is m - I know the answer is you have to
> decrease m to get overdamping, but my intuition says it should be
> opposite because it should be harder for a bigger mass to oscillate


It seems to me that "easy" and "hard" are not useful physics 
concepts in this context.  They remind me of Aristotelean 
mechanics, which many physics teachers consider the bane of
their existence.

In the absence of damping, the heavy mass oscillates just
fine, all by itself;  there's nothing easy or hard about
it.  It just is.

If you insist on talking about "easy" and "hard", you have
to be consistent.  The heavy mass is hard to get going, but
it is also /hard to stop/ ... and damping has mostly to do 
with the stopping.

=========

To approach this in serious physics terms, think about the
position and the velocity.  Consider two different masses 
with the same damping coefficient and the same velocity.
The force will be the same in both cases, but the heavy
mass will have more momentum, so it will take more time
to stop.

On 10/21/2015 02:52 PM, Jeffrey Schnick made essentially
the same point in terms of energy.

On 10/21/2015 01:35 PM, A. John Mallinckrodt pointed out
that 2m/b is the viscous stopping time-constant.

As a general rule, whenever you are the least bit confused
about a force problem, try converting it into a momentum
problem.  This applies to first-law problems, second-law
problems, and third-law problems.

So if you want to get really fancy, think about the position
and the /momentum/ as your primary variables.  Those are
the axes in phase space.  A lot of things become simpler
if you can picture them in phase space.  That includes
thermodynamics and quantum mechanics and (!) the connection
between the two.  The phase space of a harmonic oscillator
is particularly simple.

Now, consider two different masses with the same momentum.
The lighter mass will have more velocity, and therefore
more damping force (since we assume that the damping
couples to the velocity, not the momentum per se).  So
once again, the lighter mass will slow down quicker.