analytical mechanics seventh edition
p.141
3.24
let a particle of unit mass be subject to a force x-x^3 where x is its displacement from the coordinate origin
(a) Find the equilibrium points, and tell whether they are stable or unstable
(b) Calculate the total energy of the particle, and show that it is a conserved quantity
(c) Calculate the trajectories of the particle in phase space
Analytical mechanics seventh edition p.141 3.24 let a particle of unit mass be subject to a force...
Let a particle of unit mass be subject to a force
where x is its displacement from the coordinate origin and the
mass = 2 kg.
a) Derive an equation for
in terms of x.
b) Derive an equation for
, and find the equation for the phase space trajectory, y(x)
I believe Y is the equation given in the beginning of
the problem
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Consider a particle with a mass m subject to a force F(x) = ax - bx3 where x is the displacement of the origin of the reference system and a and b are positive constants. a) Find an expression of the particle's total energy. Show that this total energy is constant. b) Find the equilibrium points and determine if they are stable or unstable.
Problem 1. (24 points) A particle of mass m moving in one dimension is subject to a single conservative force with potential energy function twamions broa Listeloor stu(x) = Eo dari seoqque tenoga (1) d4 etis sauso to booga where Eo and d are positive constants. sos A (antioq 8) (0) (a) (4 points) Find the force F(x) on the particle as a function of position. lo tratto Potom odbila otvara (b) (8 points) Show that this force has equilibrium...