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How can Simple Harmonic Motion have angular frequency?

by InvalidID
Tags: angular, frequency, harmonic, motion, simple
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InvalidID
#19
Feb12-13, 01:25 PM
P: 79
Derived it!

[tex]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 } } [/tex]
WannabeNewton
#20
Feb12-13, 01:32 PM
C. Spirit
Sci Advisor
Thanks
WannabeNewton's Avatar
P: 5,446
Nice!
InvalidID
#21
Feb12-13, 01:39 PM
P: 79
[tex]F(t)=F_{ 0 }sin(ωt)[/tex]

Is there a reason why the driving oscillator in forced simple harmonic motion doesn't have a phase constant?
sophiecentaur
#22
Feb12-13, 02:04 PM
Sci Advisor
PF Gold
sophiecentaur's Avatar
P: 11,948
It would only be an added complication.


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