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Hello, I have a question about oscilations. In physics lecture, we derived a way of relating circular motion to a spring via a projection. And this made good sense, and could be applied to a horizontal spring as well, if we then shifted that circle track so that it is now verticle instead of horizontal. From there the professor went on to say, why do we give a damm about this? Yes, he loves to cruse in class its quite funny. He makes it very lively, but he is very smart :-), plus hes an old guy so that tops the cake. He then goes to show that this produces the same differnetail in terms of other things, like a pendulum, a circular spring etc. But the thing that changes is the terms that affect omega, the period. Ie. square root I/k etc. And he says that because we solved the case with striaght motion, playing that clever projection trick, we have solved the differential, and we can apply this anwser to other cases as well. The only thing i have a problem with is that for a spring thats circular, like in wristwatches, the motion cannot be described as back and forth projection, since it ticks side ways and back in arcs. But I thought about this and considered, could we not graph this side ways funny motions as a graph of theta vrs time. Then we would again obtain a sinusoidal function. ( or cosine if we wanted.) and because of this, we could solve based on this graph instead of that projection which only seems to make "sense" in that linear spring case. In the linear case could we not do the same thing, and graph the curve as displacment vrs time. And that would again be another sinusoidal curve. And we could call the distance the sin(x), but we avoid constraining ourselves to that clever projection. I think it is really the same thing, only the graph of the sine wave is "stretched" so to speak with time, if we did not graph time linearly on the x axis, then it would make that nice circle, and be a special case which is our projection.

P.S. When we talk about the amplitude, we usually talk about it in terms of hte displacement x from the origin of the springs natural equilibrium point. In the case of that coil spring, ( i think thats what you call those things.),it would not be meaningful to talk about the amplitude in terms of this displacement would it? Since the differential its d2theta/ dt2 it would be more meaninful to tlak about the amplitude in terms of the angle theta that its been displaced, not the arclength s it has been displaced, is this correct? That must be one of the things that is throwing me off with that projection analogy.

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# Oscilation Differentail equation

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