Torsional Harmonic Oscillators
For definition of terms see end of section
Torsion balances, torsion pendulums and balance wheels are examples of torsional harmonic oscillators that can oscillate with a rotational motion about the axis of the torsion spring, clockwise and counterclockwise, in harmonic motion. Their behavior is analogous to translational spring-mass oscillators (see Harmonic oscillator#Equivalent systems). The general equation of motion is:
If the damping is small, as is the case with torsion pendulums and balance wheels, the frequency of vibration is very near the natural resonant frequency of the system:
Therefore, the period is represented by:
The general solution in the case of no drive force, called the transient solution, is:
where:
Read more about this topic: Torsion Spring
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