In relation to the thread of xylophones:

When you hit a drumhead, xylophone, string, or whatever with a beater,
then, second from energy/loudness, the contact time T is the most
important parameter.  This determines the timbre.  With the impact you
inject a 'source' signal, or excitation.  The spectrum of this signal
extends roughly up to the frequency 1/T.  The energy supplied sets the
beaten device into oscillation at its various resonance frequencies,
to the extent these fall inside that frequency range of the excitation.

The general shape of the exciting pulse, as force vs. time, is not very
essential, and is anyway always about the same, the latter very much so
because contact force increases much faster than proportional to the
impression in the beater surface.

The thing you can control is the elasticity of this surface, which is
a main determinant of contact time.  Gross selection is by finding a
suitable material, e.g., from soft felt for use with a bass drum,
rubber with a steel pan, to metal with a triangle; fine tuning is by
beater radius -- piano hammers are obvious examples.

Generally you want as much noise as possible from the actuator
available, e.g., an arm, finger, pneumatic, or solenoid.  The weight
and the shaft length of the beater is selected to optimize energy
transfer from the actuator to beater head.  Another optimization is
for the weight of the beater to be in proportion to the weight of the
beaten resonator.

During the impact, an optimal contact time is about a half period of
the oscillation you want to evoke in the resonator.  If it's shorter,
then the resonator has not yet reached its maximum oscillatory velocity
when the driving pulse ends, and you do not transfer all the energy you
could have.  If it's longer, then the resonator will bounce back upon
the beater and return some of the energy just transferred to it.

A classical piano research problem was to confirm that after impact
the piano hammer should at all times go clear of the string excursions.
A reason the piano mechanism is so terribly complex is that you have to
optimize all these things simultaneously and, on top of that, for a
maximal dynamic range.

Johan Liljencrants, Stockholm

 [ The characteristics of the piano hammer are the most important
 [ factor determining the perceived 'tone' of the piano.  Building
 [ and voicing piano hammers is surely an art!  -- Robbie