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.

... We are given three particles, each of mass m, moving in one dimension and ... as well as the coordinate of each particle relative to the center of mass, ie,. ...

... is 3.4+5.4t>3.4 All four particles are all ... The particle moves along the x axis, the velocity should ... the acceleration is positive, but the particle is slowing ...

Problems Involving the Schrodinger Equation. (a) The time-independent Schrodinger equation for a free particle moving in one dimension (x) is written as (d^2 Psi ...

Please see the attached file. 1. A particle of mass m moves in one dimension in an infinite square well. Suppose that at time t=0 its wave function is. ...

... The solution is a detailed explanation on Lagrangian and Hamiltonian dynamics of a particle which moves in one dimension under the influence of a force. ...

... The time it takes the particle to reach the target once it leaves the plates is: x 1 .5 t= = = 0.25 × 106 s vx 6 × 10 6. For the particle to move 2 cm in ...

... work done W = Change in KE of the particle between the ... of the mass at height y = Work done in moving the mass ... For a system of N particles subject to a uniform ...

... As expected, equation (1.18) is the classical equation of motion of a particle that moves under the ... ¶O d 1 é ù O= O, H ú + (1.3) ih ê ë û dt ...

... always positive and the particle continues to move in that ... useful since the mass of sub-atomic particles is usually ... field and q is the charge of the particle. ...