A vibrating stretched string is one of the most fundamental physical systems where non-linear
effects play a central role. We describe results obtained with a new, dedicated experimental setup
that allows unverified details of the dynamics of this classical problem to be addressed
experimentally. The setup uniquely allows simultaneous registration of the transverse motion of the
string as well as the longitudinal tension in the string during oscillation over extended times. The
explicit non-linear connection between the string tension and the transverse oscillation amplitude
is thus directly experimentally determined, allowing us to distinguish between previously reported
diverging descriptions. For forced vibrations, frequency response curves for the transverse
amplitudes are obtained, and found to be in good agreement with predictions from a simplified model,
while the model only qualitatively reproduces the observed phases of transverse oscillation relative
to t…