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A Particle Moving In One Dimension

A particle of mass m moves in one dimension along the positive x axis. It is acted on by a constant force directed toward the origin with magnitude B, and an inverse square law repulsive force with magnitude A/x^2.

a) Find the potential energy function U(x)
b) Sketch the energy diagram for the system when the maximum kinetic energy is Ko=(1/2)mVo^2.
c) Find the equilibrium position Xo.
d) What is the frequency of small oscillation about Xo?

Solution Preview

Here is a brief explanation about how to do each part of the problem. See the attached file for details on each step.

a) To solve for U(x), we must integrate the force equation over the variable x (see attached)

When we did the integration from part a), we are left with a constant of integration. We ...

Solution Summary

The solution is comprised of a detailed explanation for the behavior of a particle moving in one dimension acted on by various forces.