Berg & Stork first state that simple harmonic motion (SHM) requires a linear restoring force. And that's apparent with things like a pendulum or a mass on a spring. However, they then describe uniform circular motion as SHM even when there's no restoring force, e.g., a mathematical point moving uniformly in a circle. So is the restoring force not really a requirement for SHM? Is all that's needed to call it SHM the fact that you can describe its motion with a sine wave (which you can do for either x or y in uniform circular motion)?