Vibrato on a long note
The first place vibrato actually earns its keep is the long, held notes of a tune you already play. Not every note — the long ones, the ones with time to bloom, usually at the top of a phrase or where it comes to rest. Short notes and open strings stay plain.
Which notes get it
How to play it
Slow, even bow. On the long C, start the note, let the vibrato grow in, and let it swell a little at the same time — grow the sound and the shimmer together. Same on the final G, then let both settle as the note ends.
Vibrato and the swell, together
Growing the sound of a long note (the messa di voce from Stage 5) and growing the shimmer at the same time is one combined gesture — and it's exactly what Louis Spohr prescribed in 1832: vibrato "on long sustained notes with dynamic swells." The two belong together. A long note that swells and shimmers and then settles is the most basic unit of lyrical playing.
Try it
Try
Take Ode to Joy or Amazing Grace — a tune you know cold. Find the two or three longest notes in it. Play the whole tune with vibrato on only those notes and everything else dead plain. It'll feel too sparse. It isn't — that's roughly how a Classical player would do it, and it already sounds like music instead of a scale.
Hear it
Listen to the opening of Bach's Air on the G String in almost any recording: the long notes are alive with vibrato, the moving notes between them much less so. The shimmer marks the arrivals.
The usual mistake
Vibrating everything the instant you can vibrate at all — the line turns to soup and the long notes lose their specialness. The opposite mistake, oddly common: vibrating the busy short notes (where it barely registers) and leaving the long notes plain (where it would matter most). Long notes first.