---
title: "An object of mass \\(m\\) on a horizontal frictionless surface is attached to a non-linear spring that exerts a restoring force \\(F(x) = -kx – cx^3\\), where \\(k\\) and \\(c\\) are positive constants and \\(x\\) is the displacement from equilibrium. The object is released from rest at position \\(x = A\\). Which of the following expressions represents the period \\(T\\) of the resulting oscillation?"
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url: "https://nerd-notes.com/ubq/117628/"
date_modified: "2026-08-04T07:49:22+00:00"
---

# An object of mass \(m\) on a horizontal frictionless surface is attached to a non-linear spring that exerts a restoring force \(F(x) = -kx – cx^3\), where \(k\) and \(c\) are positive constants and \(x\) is the displacement from equilibrium. The object is released from rest at position \(x = A\). Which of the following expressions represents the period \(T\) of the resulting oscillation?

An object of mass \(m\) on a horizontal frictionless surface is attached to a non-linear spring that exerts a restoring force \(F(x) = -kx - cx^3\), where \(k\) and \(c\) are positive constants and \(x\) is the displacement from equilibrium. The object is released from rest at position \(x = A\). Which of the following expressions represents the period \(T\) of the resulting oscillation?

- **A.** \(T = 2\sqrt{m} \int_{0}^{A} \dfrac{dx}{\sqrt{k(A^2 - x^2) + \frac{1}{2}c(A^4 - x^4)}}\)
- **B.** \(T = 4\sqrt{m} \int_{0}^{A} \dfrac{dx}{\sqrt{k(A^2 - x^2) + \frac{1}{2}c(A^4 - x^4)}}\)
- **C.** \(T = 4\sqrt{m} \int_{0}^{A} \dfrac{dx}{\sqrt{k(A^2 - x^2) + c(A^4 - x^4)}}\)
- **D.** \(T = 4\sqrt{m} \int_{0}^{A} \dfrac{dx}{\sqrt{k(A^2 - x^2) + 2c(A^4 - x^4)}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117628/*