---
title: "Along a segment of the \\(x\\)-axis, a fixed charge distribution creates an electric potential given by \\(V(x) = V_0 + b x^2\\), where \\(V_0\\) and \\(b\\) are positive constants. A small particle with mass \\(m\\) and positive charge \\(q\\) is released from rest at \\(x = x_0\\), where \\(x_0\\) is small. Which of the following expressions represents the angular frequency \\(\\omega\\) of the particle’s small oscillations about \\(x = 0\\)?"
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/118062/"
date_modified: "2026-08-04T08:04:56+00:00"
---

# Along a segment of the \(x\)-axis, a fixed charge distribution creates an electric potential given by \(V(x) = V_0 + b x^2\), where \(V_0\) and \(b\) are positive constants. A small particle with mass \(m\) and positive charge \(q\) is released from rest at \(x = x_0\), where \(x_0\) is small. Which of the following expressions represents the angular frequency \(\omega\) of the particle’s small oscillations about \(x = 0\)?

Along a segment of the \(x\)-axis, a fixed charge distribution creates an electric potential given by \(V(x) = V_0 + b x^2\), where \(V_0\) and \(b\) are positive constants. A small particle with mass \(m\) and positive charge \(q\) is released from rest at \(x = x_0\), where \(x_0\) is small. Which of the following expressions represents the angular frequency \(\omega\) of the particle's small oscillations about \(x = 0\)?

- **A.** \(\sqrt{\dfrac{q b}{2 m}}\)
- **B.** \(\sqrt{\dfrac{q b}{m}}\)
- **C.** \(\sqrt{\dfrac{2 q b}{m}}\)
- **D.** \(\sqrt{\dfrac{4 q b}{m}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118062/*