Torsion is a twisting motion, imagine grabbing each end of a rod in your hands and twisting them in opposite directions. If you have something where the torsion is oscillating it will be twisting one way and then twisting the other way. The torsional vibration frequency is the the frequency of this oscillation between twisting directions.
Look up the Tacoma narrows bridge disaster. The bridge was made of concrete and steel and cables, but overall it behaved like a “ribbon”, twisting left and right in the winds. After all, it was just suspended by a bunch of cables. It just so happened that the frequency of winds over the water was roughly the same as this twisting (aka torsional) frequency. So even tiny twisting motions were amplified by the winds and the whole bridge twisted so much that cables snapped and the whole thing fell.
Imagine a clock pendulum, it swings backwards and forwards at a fixed frequency. Gravity is always trying to return the pendulum to the centre. Now imagine the same pendulum without gravity – it wouldn’t work. But if you add a torsion spring at the pivot that tries to return the pendulum to the centre then it will work! The system of pendulum plus torsion spring will swing backwards and forwards (oscillate) at a fixed frequency. Change the stiffness of the spring (or the mass of the pendulum) and you will change the frequency.
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