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#9
Feb12-13, 11:37 AM
P: 79
I've realized that a lot of simple harmonic motion is basically periodic motion in which the restoring force is proportional to the position away from the equilibrium. Does that mean all simple harmonic motion can be modelled using a spring?

The equation:

[tex]ω=\sqrt { \frac { k }{ m } }[/tex]

applies to simple harmonic motion when a spring is involved where k is the spring constant. But k doesn't need to be the spring constant right? It just needs to be the proportional constant of the restoring force to the displacement, right?

[tex]k=\frac { F }{ x }[/tex]

where F is any restoring force.

Now my question is: is this ever useful when dealing with simple harmonic motion problem where the question doesn't involve a spring? The issue is that problems don't give you the proportional constant of the restoring force to the displacement when there is no spring involved I'm assuming?

[tex]θ(t)={ θ }_{ max }cos(ωt+ϕ)[/tex]

Does θmax need to be in radians or degrees? It doesn't matter, does it? Will it matter if I take the derivative?

[tex]w(t)={ -θ }_{ max }ωsin(ωt+ϕ)[/tex]

How can angular speed be a function of itself?