I think I understand what you're getting at now; before I thought you were criticizing my use of a slinky spring. This is where things got a little confusing for me because looking further, there appeared to be at least two possible expressions for the wave velocity in a steel wire:
##v_p =...
The stiffness ##k = AE/L## where ##A## is the cross sectional area, ##E## is Young's modulus and ##L## is the length. Young's modulus ##E = \sigma/\epsilon## where ##\sigma## is the uniaxial force per unit area, and ##\epsilon## is the change in length divided by the original length.
##v_p##...
I'm not sure, it was just a suggestion to get my picture of a finite ##v_p## across. Another suggestion would be steel wire giving ##v_p = \sqrt{\frac{T}{\rho}}## where ##\rho## is the linear mass density.
Your spring model assumes a wave velocity ##v_p = \infty## which means energy can be transported through the spring infinitely fast; whereas I'm thinking of something like a slinky spring with a finite ##v_p## transporting energy at a finite rate. Let's say the oscillations have died down and...
I have a question that appears elementary, but bizarre in its conclusion:
A mass ##M## is accelerated by a spring of length ##L##, wave-speed ##v_p##, spring-constant ##K## and a constant force ##F## at the other end. As ##K## increases, the extension of the spring ##dx## decreases as does the...