The "classical" circular motion is strongly related to periodic motion, so it is in the OP's best interest to study circular motion as it relates to the topics above
Very true Cawolf. Uniform circular motion may have a period (and frequency), but the passages and questions associated with it are very different from the ones with pendula and springs.
In our class, we lightly touch on the work and energy associated with uniform circular motion versus work and energy of comparable systems, but have omitted the bulk of it (alpha, omega, etc...). So far no student has come back complaining about that omission.
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