Page "Balance spring" Paragraph 21

A balance spring obeys Hooke's Law: the restoring torque is proportional to the angular displacement.

When this property is exactly satisfied, the balance spring is said to be isochronous, and the period of oscillation is independent of the amplitude of oscillation.

This is an essential property for accurate timekeeping, because no mechanical drive train can provide absolutely constant driving force.

This is particularly true in watches and portable clocks which are powered by a mainspring, which provides a diminishing drive force as it unwinds.

Another cause of varying driving force is friction, which varies as the lubricating oil ages.