Period of Oscillation
The balance spring is an essential part of the balance wheel; together they form a harmonic oscillator. The balance spring provides the linear restoring force that reverses the motion of the wheel so it oscillates back and forth. The motion of the balance wheel is approximately simple harmonic motion, i.e., a sinusoidal motion of constant period. Its resonant period is resistant to changes from perturbing forces, which is what makes it a good timekeeping device. The stiffness of the spring, its spring coefficient, in N-m/radian, along with the balance wheel's moment of inertia, in kg-m2, determines the wheel's oscillation period in seconds:
This period controls the rate of the timepiece.
Read more about this topic: Balance Spring
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