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RockenNS42
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Homework Statement
The motion of a linear oscillator may be represented by means of a graph in which x is abscissa and dx/dt as ordinate. The histroy of the oscillator is then a curve
a)show that for an undamped oscillator this curve is an ellipse
b) show (at least qualitatively) that if a damping curve is introduced on gets a curve spiraling into origin.
Homework Equations
The Attempt at a Solution
a) I got that
x(t)=Asin(wt-α)
v(t)=wAcos(wt-α)
Another student told me to "elimate the t's" to get
x2/A2 +X2/(Aw)2 =1
and that is total energy is E=1/2KA2 and w2=k/m then
x2/(2E/k) +X2/(2E/m) =1First of all, I don't under stand how eliminated his t's. I do get that he found the eq of an ellipse, but how do I go from an eq with X and w to one with x and dx/dt?
b)I have no sweet clue