Hi all,
this is my first time on PF.
I do not know English but I have a problem of a harmonic oscillator.
I have rather large head, help me please , I do not know what else to do ...
I have this problem:
Consider the harmonic oscillator with an additional repulsive
cubic force, whose potential is U(q1)=[itex]\frac{k}{2}[/itex]*[itex]q1^{2}[/itex] - k'[itex]q1^{4}[/itex], (k, k > 0), and study all
possible solutions, periodic and non-periodic.
I do know the Hamiltonian and the equation solution of the system, giving
q1*=[itex]\sqrt{1/2}[/itex][itex]\int(dq1/\sqrt{(E/m)-U(q1)})[/itex]
I tried to do it by trigonometric substitution but does not work, i do not know if anyone could give me some idea of how I can solve, I'll be very grateful.
this is my first time on PF.
I do not know English but I have a problem of a harmonic oscillator.
I have rather large head, help me please , I do not know what else to do ...
I have this problem:
Consider the harmonic oscillator with an additional repulsive
cubic force, whose potential is U(q1)=[itex]\frac{k}{2}[/itex]*[itex]q1^{2}[/itex] - k'[itex]q1^{4}[/itex], (k, k > 0), and study all
possible solutions, periodic and non-periodic.
I do know the Hamiltonian and the equation solution of the system, giving
q1*=[itex]\sqrt{1/2}[/itex][itex]\int(dq1/\sqrt{(E/m)-U(q1)})[/itex]
I tried to do it by trigonometric substitution but does not work, i do not know if anyone could give me some idea of how I can solve, I'll be very grateful.
