---
title: "A particle of mass \\(m\\) moves along the positive \\(x\\)-axis in a region where its potential energy is given by \\(U(x) = \\dfrac{A}{x^2} – \\dfrac{B}{x}\\), where \\(A\\) and \\(B\\) are positive constants. The particle is displaced slightly from its stable equilibrium position and released from rest. What is the angular frequency \\(\\omega\\) of the resulting small-amplitude oscillations in terms of \\(A\\), \\(B\\), and \\(m\\)?"
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url: "https://nerd-notes.com/ubq/120963/"
date_modified: "2026-08-23T04:44:47+00:00"
---

# A particle of mass \(m\) moves along the positive \(x\)-axis in a region where its potential energy is given by \(U(x) = \dfrac{A}{x^2} – \dfrac{B}{x}\), where \(A\) and \(B\) are positive constants. The particle is displaced slightly from its stable equilibrium position and released from rest. What is the angular frequency \(\omega\) of the resulting small-amplitude oscillations in terms of \(A\), \(B\), and \(m\)?

A particle of mass \(m\) moves along the positive \(x\)-axis in a region where its potential energy is given by \(U(x) = \dfrac{A}{x^2} - \dfrac{B}{x}\), where \(A\) and \(B\) are positive constants. The particle is displaced slightly from its stable equilibrium position and released from rest. What is the angular frequency \(\omega\) of the resulting small-amplitude oscillations in terms of \(A\), \(B\), and \(m\)?

- **A.** \(\sqrt{\dfrac{B^4}{mA^3}}\)
- **B.** \(\sqrt{\dfrac{B^4}{4mA^3}}\)
- **C.** \(\sqrt{\dfrac{B^4}{8mA^3}}\)
- **D.** \(\sqrt{\dfrac{5B^4}{8mA^3}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120963/*