---
title: "A particle of mass \\(m\\) and positive charge \\(+q\\) is constrained to move in the \\(xy\\)-plane within a region of electrostatic potential given by \\(V(x, y) = V_0 \\big(2 – \\cos(kx) – \\cos(ky)\\big)\\), where \\(V_0\\) and \\(k\\) are positive constants. The particle is released from rest near the origin at a small initial displacement \\((x_0, y_0)\\), where \\(kx_0 \\ll 1\\) and \\(ky_0 \\ll 1\\). Which of the following expressions represents the angular frequency \\(\\omega\\) of the particle’s resulting small oscillations?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/118081/"
date_modified: "2026-08-04T08:05:02+00:00"
---

# A particle of mass \(m\) and positive charge \(+q\) is constrained to move in the \(xy\)-plane within a region of electrostatic potential given by \(V(x, y) = V_0 \big(2 – \cos(kx) – \cos(ky)\big)\), where \(V_0\) and \(k\) are positive constants. The particle is released from rest near the origin at a small initial displacement \((x_0, y_0)\), where \(kx_0 \ll 1\) and \(ky_0 \ll 1\). Which of the following expressions represents the angular frequency \(\omega\) of the particle’s resulting small oscillations?

A particle of mass \(m\) and positive charge \(+q\) is constrained to move in the \(xy\)-plane within a region of electrostatic potential given by \(V(x, y) = V_0 \big(2 - \cos(kx) - \cos(ky)\big)\), where \(V_0\) and \(k\) are positive constants. The particle is released from rest near the origin at a small initial displacement \((x_0, y_0)\), where \(kx_0 \ll 1\) and \(ky_0 \ll 1\). Which of the following expressions represents the angular frequency \(\omega\) of the particle's resulting small oscillations?

- **A.** \(k \sqrt{\dfrac{q V_0}{m}}\)
- **B.** \(k \sqrt{\dfrac{2q V_0}{m}}\)
- **C.** \(2k \sqrt{\dfrac{q V_0}{m}}\)
- **D.** \(\dfrac{k}{2} \sqrt{\dfrac{q V_0}{m}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118081/*