---
title: "A particle of mass \\(m\\) moves along the x-axis in a potential energy field given by \\(U(x) = U_0 \\left( e^{-2ax} – 2e^{-ax} \\right)\\), where \\(U_0\\) and \\(a\\) are positive constants. The particle is displaced slightly from its stable equilibrium position and released. Which of the following expressions represents the period \\(T\\) of the resulting small oscillations?"
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url: "https://nerd-notes.com/ubq/117578/"
date_modified: "2026-08-04T07:49:11+00:00"
---

# A particle of mass \(m\) moves along the x-axis in a potential energy field given by \(U(x) = U_0 \left( e^{-2ax} – 2e^{-ax} \right)\), where \(U_0\) and \(a\) are positive constants. The particle is displaced slightly from its stable equilibrium position and released. Which of the following expressions represents the period \(T\) of the resulting small oscillations?

A particle of mass \(m\) moves along the x-axis in a potential energy field given by \(U(x) = U_0 \left( e^{-2ax} - 2e^{-ax} \right)\), where \(U_0\) and \(a\) are positive constants. The particle is displaced slightly from its stable equilibrium position and released. Which of the following expressions represents the period \(T\) of the resulting small oscillations?

- **A.** \(\dfrac{\pi}{a}\sqrt{\dfrac{m}{U_0}}\)
- **B.** \(\dfrac{2\pi}{a}\sqrt{\dfrac{m}{U_0}}\)
- **C.** \(\dfrac{2\pi}{a}\sqrt{\dfrac{m}{2U_0}}\)
- **D.** \(\dfrac{2\pi}{a}\sqrt{\dfrac{2m}{U_0}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117578/*