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Re: No stiffness effect



As I wrote on Friday, the measured v of a transverse wave in
a spring (stretched from 3 meters to 9 meters with the tension
force of 15 N) was found to agree (plus or minus about 1 %)
with the textbook formula v=sqr(T/mu).

Here are my questions.

1) A long spring is often idealized as a system of n point
masses connected by n-1 massless springs. Is the spring
stiffness, ST, automatically eliminated by this idealization?
(John defined stiffness as "the spring constant for flexion"
rather than for extension. If it takes 2 N to pull a coil
sidewise by 0.01 m, and 4 N to pull it by 0.02 m, then
ST= 2/0.01=200 N/m. Right?).

2) If ST is not automatically eliminated then how to calculate
it, for a given idealized structure? For example, 2000 point
masses (0.1 kg each) on a horizontal frictionless surface
connected with 1999 relaxed springs (each L=0.2 m and
k=30 N/m) along the x axis. There is no tension.

3) Suppose the last mass is attached to a rigid wall while the
first mass is wiggled harmonically at f=4 Hz. What is the
formula for v (of the transverse stiffness wave at that f)?
Ludwik Kowalski