Pendulums and balance wheels are both harmonic oscillators, but thats kind of where the similarities end. For a pendulum, the restoring force is gravity, whereas for the balance wheel, the spring force is the restoring force.
@Theognosis Hodinkee definitely has it pretty wrong on this one, since the major difference is clearly not portability, as Archer said – one literally relies on gravity to function, while gravity is a hindrance to the other.
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