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27 Nov 2019
(Fowles & Cassiday, Problem 3.24) Let a particle of unit massbe subject to a force
x - x^3, where x is its displacement from the coordinateorigin.
(a) Find the equilibrium points, and tell whether they are stableor unstable.
(b) Calculate the total energy of the particle, and show that it isa conserved quantity. (Hint for this problem: Let y = dx/dt , andwrite dy/dx = (dy/dt)/(dx/dt). By separation of variables,integrate to find a relation between y and x. Compare this to E = T+ V .)
(c) Calculate the trajectories of the particle in phase space. (Youessentially did this
above by finding the relation between y and x; you should be ableto express the
paths in terms of the energy.)
(Fowles & Cassiday, Problem 3.24) Let a particle of unit massbe subject to a force
x - x^3, where x is its displacement from the coordinateorigin.
(a) Find the equilibrium points, and tell whether they are stableor unstable.
(b) Calculate the total energy of the particle, and show that it isa conserved quantity. (Hint for this problem: Let y = dx/dt , andwrite dy/dx = (dy/dt)/(dx/dt). By separation of variables,integrate to find a relation between y and x. Compare this to E = T+ V .)
(c) Calculate the trajectories of the particle in phase space. (Youessentially did this
above by finding the relation between y and x; you should be ableto express the
paths in terms of the energy.)
