---
title: "A particle of mass \\(m\\) moves along the \\(x\\)-axis in a potential energy field given by \\(U(x) = kx^4\\), where \\(k\\) is a positive constant. Which of the following correctly gives the force \\(F(x)\\) acting on the particle and explains why the resulting motion is not simple harmonic motion?"
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url: "https://nerd-notes.com/ubq/117563/"
date_modified: "2026-08-04T07:49:06+00:00"
---

# A particle of mass \(m\) moves along the \(x\)-axis in a potential energy field given by \(U(x) = kx^4\), where \(k\) is a positive constant. Which of the following correctly gives the force \(F(x)\) acting on the particle and explains why the resulting motion is not simple harmonic motion?

A particle of mass \(m\) moves along the \(x\)-axis in a potential energy field given by \(U(x) = kx^4\), where \(k\) is a positive constant. Which of the following correctly gives the force \(F(x)\) acting on the particle and explains why the resulting motion is not simple harmonic motion?

- **A.** \(F(x) = 4kx^3\), because the force is equal to the spatial derivative of the potential energy.
- **B.** \(F(x) = -\dfrac{1}{5}kx^5\), because force is equal to the negative spatial integral of the potential energy.
- **C.** \(F(x) = -4kx^3\), because simple harmonic motion requires a restoring force directly proportional to the negative of displacement.
- **D.** \(F(x) = -kx^3\), because the non-linear force prevents mechanical energy from being conserved during oscillation.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117563/*