I haven't tried this, so I am making it up as I go along.
This is a hypothesis you can test:
Here's one way to measure the horizontal displacement: Glue
a vernier caliper to the guitar, under the strings, so that
the jaw-motion runs perpendicular to the strings.
A $3.00 plastic caliper should do.
Second-best idea: To reduce parallax error, glue a mirror to
the sliding jaw.
Better idea: Glue a metal peg to the side of the sliding jaw,
something like a thumbtack. The peg sticks up high enough to
touch the string. It is connected via a thin flexible wire
to a touch-detector circuit. Move the jaw so that the peg
just barely touches the string at equilibrium. Record the
reading. Then move the peg to another position, maybe
10 ± 0.1 mm away. Measure the transverse force needed to
deflect the string that much.
This has the advantage that the thickness of the string drops
out of the measurement.
This stands in contrast to the spoke tensionometer mentioned
in my previous message, where you have to apply a correction
to account for spoke thickness. The exist more-accurate and
easier-to-use tensionometers, but they cost a gazillion bucks;
don't ask me why.
Also the touch-detector is vastly more sensitive than trying
to eyeball the position. Measuring the force at 0, 5, 8, and
10 mm gives you a consistency check on the theory, and on the
procedure. This is not necessary every time, but worth
doing at least once.
I reckon that measuring the horizontal displacement is always
going to be the dominant contribution to the uncertainty.
Everything else can easily be measured to better than 1%.
So my thinking is, measure the deflection as best we can
without making things unduly complicated.
The tension measurement is indirect, which is a conceptual
burden for the students ... but note that even with the
PASCO device the tension measurement is somewhat indirect.
Warn students that the transverse displacement-versus-force
relationship absolutely positively does *NOT* obey Hooke's
law. Hint: Principle of Virtual Work, plus simple geometry
(a^2 + b^2 = c^2).
The Mythbusters, non-scientists that they are, had to find
this out the hard way. When they wanted to build a suspension
bridge, on the first attempt they tried to make it nice and
horizontal, not saggy. That incurs a mechanical disadvantage,
by a factor of infinity. Oooops. Apparently they never
wondered why a suspension bridge (such as the Brooklyn Bridge
or the Golden Gate Bridge) is built with majestic tall towers
supporting saggy catenaries...........
One of the costs of experimenting with real-world things is
that sometimes there are nonlinearities or even nonidealities.
OTOH IMHO in this case the nonlinearity is interesting, and
well worth knowing about, so this is a feature, not a bug.