Electromagnet Options to Vibrate Long String at 80Hz
In the case of a string, it will be resonant. 

You can probably use a pair of supermagnets either side of the string (old hard drive) , and put your AC current through the string.  You want a heavy guitar/bass string. In fact get a guitar and start playing with that on the bass string.

The string is the electromagnet. The magnets field must be across the string (i.e. these magnets are attracting each other), and this makes the string move from side to side, parallel to the gap as you pass current though it.

The magnets will be down fairly close to the nut or bridge. Here are two small 3/8" fridge super magnets, held 3.2mm apart with some hotmelt. The signal generator is connected to each end of the string, and is putting 130mA through the string.

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It is very hard to tune the signal generator onto the fundamental, the resonance is so narrow - about 0.2Hz at 100Hz

You cannot make a string move, except in a resonant fashion. Away from its resonant frequency it just sits there - that's what resonance is all about. 

This also means that you have to make the string set the frequency, not the electronics. 

You can also do it mechanically see Wheel Harp or Hurdy Gurdy. You could also make a little plucker than plucks it every few seconds - which would give the satisfying view of the vibration decaying.

BTW, the challenge of this is making a strobe frequency that is 0.3Hz off from the strings frequency.

Another approach is the skipping rope one.

Yet another is to use flourescent nylon for your string (Weed whipper line), and UV/Blue leds for the strobe. (attach a tiny super magnet to the line, or use hard-drive coil, or loudspeaker cone etc etc)