Pedal Dampening
One of the unique and incredibly useful attributes of a vibraphone is its ability to dampen with a pedal. Though its certainly a simpler mechanism than a piano, its basic function of using felt to mute a sound remains the same. This can be notated in the same fashion as a piano, using standard markings:

In a case like the above, the markings might not be entirely necessary; the half notes imply that the notes are to resonate, or be played with the pedal down. It’s nice, however, to have clarity on where exactly to lift the pedal. This is more useful in more complicated passages where the pedaling might not be as clearly implied. Some composers opt to not use any markings, and prefer to leave the decision to the performer.
Remember that a free foot is needed to control the pedal, so be wary of parts requiring lots of pedal in a piece with other foot percussion.
Mallet/Hand dampening
Anything that stops bar(s) from vibrating is a form of dampening. This is particularly useful when you want some notes to ring, and others to be muted.
So how should this be notated? It’s ideal to indicate rhythmically where the cutoff should happen, which is achieved by using x note heads in the desired spot. This is illustrated in the two examples below; one with a normal pedal marking, and one using l.v. marks on the notes that are to ring. Since these don’t include a pedal up marking, they’d both ring indefinitely.


Mallets can also be used to dampen at the same time that another is played, like so:

All damp all the time
This isn’t hard; just don’t use the pedal. But clarify that in your score! A lot of players will take no markings as an invitation to experiment with pedaling. A quick note at the beginning to clarify what you want can save everyone some time.
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