the period is represented by:

The general solution in the case of no drive force (), called the transient solution, is:

where:

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Applications

The balance wheel of a mechanical watch is a harmonic oscillator whose resonant frequency sets the rate of the watch. The resonant frequency is regulated, first coarsely by adjusting with weight screws set radially into the rim of the wheel, and then more finely by adjusting with a regulating lever that changes the length of the

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