The potential energy of a conservative force is U(x) = ax?-bx", with a and b positive constant parameters. (a) Find the equilibrium points and discuss whether these points are stable or unstable (and why). (b) At time t=0, a particle with mass m and initial velocity vin=0 is placed at a distance xin close to the stable equilibrium point. Assume that xXin is very small compared with the distance between the stable and the unstable equilibrium points. Find an approximate expression for the period of oscillations of the mass m. (c) A second particle with mass M is placed, at time t=0, at the exact position of the stable equilibrium point, with a non-zero initial velocity vin. Find the minimum value of vin such that the particle can travel a distance at least equal to the distance between the stable equilibrium point and the nearest unstable equilibrium point. This problem must be solved symbolically, numbers are not required.

The potential energy of a conservative force is U(x) = ax?-bx", with a and b positive constant parameters. (a) Find the equilibrium points and discuss whether these points are stable or unstable (and why). (b) At time t=0, a particle with mass m and initial velocity vin=0 is placed at a distance xin close to the stable equilibrium point. Assume that xXin is very small compared with the distance between the stable and the unstable equilibrium points. Find an approximate expression for the period of oscillations of the mass m. (c) A second particle with mass M is placed, at time t=0, at the exact position of the stable equilibrium point, with a non-zero initial velocity vin. Find the minimum value of vin such that the particle can travel a distance at least equal to the distance between the stable equilibrium point and the nearest unstable equilibrium point. This problem must be solved symbolically, numbers are not required.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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