Although the hammer is meant to impart only vertical motion in the string of a grand piano, eventually horizontal motion also occurs. Horizontal motion is less damped over time because its motion is less coupled to the piano bridge and ergo, soundboard. ²¹¹

The coupling of the Stuart piano string by the bridge agraffe fastens the string in an up-down vertical plane. When the hammer strikes the string in the vertical up direction, the Stuart string oscillates reduced levels of damping in comparison to the Steinway string. This is because the Steinway string is pinned to the bridge in a horizontal plane, and will not enter into its vertical oscillation as easily as the Stuart string.

A vibrating system whose amplitude decreases in this way is said to be damped, and the rate of decrease is the damping constant. ²¹²
If the oscillator is heavily damped, the transient motion decays rapidly, and the oscillator quickly settles into its steady-state motion. If the damping is small, however, the transient behaviour may continue for many cycles of oscillation.²¹³

Onset – reduced damping

In the tests conducted in chapter two on the influences of coupling on vibration, the initial vertical oscillation of the Stuart string was found to be significantly larger than the Steinway’s. In this instance we established proof that the Stuart string was vibrating in a mode of reduced damping. The decay curves and spectrograms illustrated in chapter four, reveal that the majority of Stuart oscillations examined lose more energy than the Steinway oscillations in the initial .5s onset state, shown by steeper decay and amplitude curves. The majority of Stuart sounds produced higher amplitudes in this onset period. Given that each sound is struck with the same calibrated force, this also provides evidence of reduced damping in the Stuart coupling set up, the bridge agraffe.

After-sound – reduced damping

The decay curves and spectrograms illustrated in chapter four show the majority of Stuart sounds arrive at the settled after-sound period of oscillation earlier than Steinway. The string vibration tests in chapter 2, confirmed that the Stuart string maintained less of a horizontal vibration in its after-sound oscillation than Steinway. This shows the Stuart string vibration experienced less change in its overall vibration contour than Steinway. At the change of vibration mode from the vertical oscillation to its less-horizontal ²¹⁴ elliptical oscillation, it was found that the Stuart string lost less energy than the Steinway string. Subsequently the rate of decay of the Stuart sound in its after-sound state, is observed to be slower and the audible perception is one of a sound with more sustain.

²¹¹Dean Livelybrooks, “ The Piano” Physics of Sound,Essentials of Physics- PHYS 152Lecture 16 The Piano (blog). http://hendrix2.uoregon.edu/~dlivelyb/phys152/l16.html,2007, accessed May, 2015.
²¹²Thomas Rossing, Moore, R. Wheeler, P. The Science of Sound, 3rd Ed. (USA: Addison-Wesley, 2001),25.
^{213     5}Fletcher& Rossing , 21.
²¹⁴‘less horizontal’ in comparison to the Steinway string oscillation