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## How can Simple Harmonic Motion have angular frequency?

It isn't making any intuitive sense. If it isn't moving in circular motion, how can it have angular frequency or speed?

Also,

$$v=\pm ω\sqrt { A^{ 2 }-x^{ 2 } }$$

only applies to SHM with springs only, right?

Also, does anyone know how to derive this equation below?

$$x=\frac { \pm \sqrt { { { v }_{ max } }^{ 2 }+{ v }^{ 2 } } }{ ω }$$
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