---
title: "An object of mass \\(m\\) is attached to an ideal spring and undergoes simple harmonic motion along the \\(x\\)-axis with amplitude \\(x_0\\) and angular frequency \\(\\omega\\). The net acceleration of the object at any position \\(x\\) is given by \\(a(x) = -\\omega^2 x\\). Which of the following best describes the shape of the graph of the object’s velocity \\(v\\) as a function of position \\(x\\) over one full cycle of oscillation?"
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url: "https://nerd-notes.com/ubq/120961/"
date_modified: "2026-08-23T04:44:45+00:00"
---

# An object of mass \(m\) is attached to an ideal spring and undergoes simple harmonic motion along the \(x\)-axis with amplitude \(x_0\) and angular frequency \(\omega\). The net acceleration of the object at any position \(x\) is given by \(a(x) = -\omega^2 x\). Which of the following best describes the shape of the graph of the object’s velocity \(v\) as a function of position \(x\) over one full cycle of oscillation?

An object of mass \(m\) is attached to an ideal spring and undergoes simple harmonic motion along the \(x\)-axis with amplitude \(x_0\) and angular frequency \(\omega\). The net acceleration of the object at any position \(x\) is given by \(a(x) = -\omega^2 x\). Which of the following best describes the shape of the graph of the object's velocity \(v\) as a function of position \(x\) over one full cycle of oscillation?

- **A.** A parabola centered on the \(v\)-axis with vertex at \((0, \omega x_0)\) and \(x\)-intercepts at \(\pm x_0\)
- **B.** A hyperbola centered at the origin with vertices at \((\pm x_0, 0)\) and asymptotes \(v = \pm \omega x\)
- **C.** An ellipse centered at the origin with \(x\)-intercepts at \(\pm x_0\) and \(v\)-intercepts at \(\pm \omega x_0\)
- **D.** A sinusoidal curve oscillating symmetrically between \(v = -\omega x_0\) and \(v = \omega x_0\) with a spatial period of \(2x_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120961/*