---
title: "A particle of mass \\(m = 0.25 \\text{ kg}\\) moves along the \\(x\\)-axis in a conservative force field with potential energy given by \\(U(x) = U_0 \\cosh(bx)\\), where \\(U_0 = 4.0 \\text{ J}\\) and \\(b = 3.0 \\text{ m}^{-1}\\). The particle is displaced slightly from its stable equilibrium position at \\(x = 0\\) and released from rest. Given that \\(\\dfrac{d}{dx}[\\cosh(bx)] = b\\sinh(bx)\\), \\(\\dfrac{d}{dx}[\\sinh(bx)] = b\\cosh(bx)\\), and \\(\\cosh(0) = 1\\), what is the angular frequency of the resulting small-amplitude oscillations?"
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url: "https://nerd-notes.com/ubq/123990/"
date_modified: "2026-09-28T13:30:00+00:00"
---

# A particle of mass \(m = 0.25 \text{ kg}\) moves along the \(x\)-axis in a conservative force field with potential energy given by \(U(x) = U_0 \cosh(bx)\), where \(U_0 = 4.0 \text{ J}\) and \(b = 3.0 \text{ m}^{-1}\). The particle is displaced slightly from its stable equilibrium position at \(x = 0\) and released from rest. Given that \(\dfrac{d}{dx}[\cosh(bx)] = b\sinh(bx)\), \(\dfrac{d}{dx}[\sinh(bx)] = b\cosh(bx)\), and \(\cosh(0) = 1\), what is the angular frequency of the resulting small-amplitude oscillations?

A particle of mass \(m = 0.25 \text{ kg}\) moves along the \(x\)-axis in a conservative force field with potential energy given by \(U(x) = U_0 \cosh(bx)\), where \(U_0 = 4.0 \text{ J}\) and \(b = 3.0 \text{ m}^{-1}\). The particle is displaced slightly from its stable equilibrium position at \(x = 0\) and released from rest. Given that \(\dfrac{d}{dx}[\cosh(bx)] = b\sinh(bx)\), \(\dfrac{d}{dx}[\sinh(bx)] = b\cosh(bx)\), and \(\cosh(0) = 1\), what is the angular frequency of the resulting small-amplitude oscillations?

- **A.** \(12 \text{ rad/s}\)
- **B.** \(24 \text{ rad/s}\)
- **C.** \(36 \text{ rad/s}\)
- **D.** \(144 \text{ rad/s}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123990/*