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## How can Simple Harmonic Motion have angular frequency?

 Quote by InvalidID If it isn't moving in circular motion, how can it have angular frequency or speed?
See the section of this video from about 1:45 to 2:07. It demonstrates the connection between SHM and uniform circular motion.

 Derived it! $$TE={ KE }+PE\quad and\quad TE={ KE }_{ max }={ PE }_{ max }\\ \\ { KE }_{ max }=KE+PE\\ \frac { 1 }{ 2 } m{ { v }_{ max } }^{ 2 }=\frac { 1 }{ 2 } m{ { v } }^{ 2 }+\frac { 1 }{ 2 } k{ x }^{ 2 }\\ m{ { v }_{ max } }^{ 2 }=m{ { v } }^{ 2 }+k{ x }^{ 2 }\\ k{ x }^{ 2 }=m{ { v }_{ max } }^{ 2 }-m{ { v } }^{ 2 }\\ { x }^{ 2 }=\frac { m }{ k } ({ { v }_{ max } }^{ 2 }-{ { v } }^{ 2 })\\ { x }^{ 2 }={ ω }^{ -2 }({ { v }_{ max } }^{ 2 }-{ { v } }^{ 2 })\\ x=\pm \sqrt { { ω }^{ -2 }({ { v }_{ max } }^{ 2 }-{ { v } }^{ 2 }) } \\ x=\pm \frac { \sqrt { { { v }_{ max } }^{ 2 }-{ { v } }^{ 2 } } }{ { ω } }$$
 $$F(t)=F_{ 0 }sin(ωt)$$ Is there a reason why the driving oscillator in forced simple harmonic motion doesn't have a phase constant?