I’m probably just not thinking about things clearly, but the following seems unintuitive to me.
Imagine a mass m on a spring k in a viscous fluid so that we have Stokes’ drag -bv where v is the velocity of the object.
Okay we know how this all goes. If we start with values of m, k, and b all near 1 (in usual units of m, kg, s) we are near the critical damping limit. Now let’s imagine changing one parameter and seeing what happens:
* if we increase b, we get overdamping - that makes sense because the fluid is more viscous and so it’s harder for the mass to oscillate through it
* if we decrease k, we get overdamping - that makes sense because the spring is too weak to overcome the drag
* 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
Which of course it is. It’s just that the drag properly normalized decreases less rapidly than the natural frequency decreases, as one decreases m, so the drag always eventually wins.
To put it mathematically, in the limit of small enough m, sqrt(k/m) < b/2m is guaranteed to hold (if k and b are held constant).
So I guess my real question is: Why intuitively does the effective “drag frequency” (if I can call b/2m that) depend on the object’s mass?
To put it another way: What is an appropriate intuitive way of understanding b/2m? I know mathematically it has units of frequency. But what does that mean physically?