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IWantToLearn
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Hi,
i was studying Classical Mechanics course introduced by the brilliant Prof. V. Balakrishnan
he was studying the phase portrait of a simple harmonic oscillator in one dimension , where the total enegry of the system is E=[itex]\frac{1}{2}[/itex]m[itex]\dot{q}[/itex][itex]^{2}[/itex]+[itex]\frac{1}{2}[/itex]mω[itex]^{2}[/itex]q[itex]^{2}[/itex] where E is constant.
in minute 54 he suggested to change the sign of the potential to be negative:
E=[itex]\frac{1}{2}[/itex]m[itex]\dot{q}[/itex][itex]^{2}[/itex]-[itex]\frac{1}{2}[/itex]mω[itex]^{2}[/itex]q[itex]^{2}[/itex]
the motion is not harmonic any more and the potential well is inverted to be opened in the negative y-direction, he asked to complete the phase portrait for this new motion,
i tried to think of it physically and i was half way to get it, but i failed,
here is the solution http://www-physics.ucsd.edu/students/courses/fall2010/physics200a/LECTURES/200_COURSE.pdf page 32
the reason that i failed is that i couldn't able to know why the parabola was rotated to be symmetric around the x-axis?
i was studying Classical Mechanics course introduced by the brilliant Prof. V. Balakrishnan
he was studying the phase portrait of a simple harmonic oscillator in one dimension , where the total enegry of the system is E=[itex]\frac{1}{2}[/itex]m[itex]\dot{q}[/itex][itex]^{2}[/itex]+[itex]\frac{1}{2}[/itex]mω[itex]^{2}[/itex]q[itex]^{2}[/itex] where E is constant.
in minute 54 he suggested to change the sign of the potential to be negative:
E=[itex]\frac{1}{2}[/itex]m[itex]\dot{q}[/itex][itex]^{2}[/itex]-[itex]\frac{1}{2}[/itex]mω[itex]^{2}[/itex]q[itex]^{2}[/itex]
the motion is not harmonic any more and the potential well is inverted to be opened in the negative y-direction, he asked to complete the phase portrait for this new motion,
i tried to think of it physically and i was half way to get it, but i failed,
here is the solution http://www-physics.ucsd.edu/students/courses/fall2010/physics200a/LECTURES/200_COURSE.pdf page 32
the reason that i failed is that i couldn't able to know why the parabola was rotated to be symmetric around the x-axis?
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