---
title: "An object of mass \\(0.50\\text{ kg}\\) attached to an ideal horizontal spring undergoes simple harmonic motion on a frictionless surface. The graph shows the potential energy \\(U(x)\\) of the system and the total mechanical energy \\(E\\) of the object-spring system as functions of position \\(x\\).  What is the magnitude of the acceleration of the object when it is at position \\(x = 0.30\\text{ m}\\)?"
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url: "https://nerd-notes.com/ubq/121003/"
date_modified: "2026-08-23T04:45:08+00:00"
---

# An object of mass \(0.50\text{ kg}\) attached to an ideal horizontal spring undergoes simple harmonic motion on a frictionless surface. The graph shows the potential energy \(U(x)\) of the system and the total mechanical energy \(E\) of the object-spring system as functions of position \(x\).

What is the magnitude of the acceleration of the object when it is at position \(x = 0.30\text{ m}\)?

An object of mass \(0.50\text{ kg}\) attached to an ideal horizontal spring undergoes simple harmonic motion on a frictionless surface. The graph shows the potential energy \(U(x)\) of the system and the total mechanical energy \(E\) of the object-spring system as functions of position \(x\).

What is the magnitude of the acceleration of the object when it is at position \(x = 0.30\text{ m}\)?

![A 2D quantitative Cartesian graph with gridlines. The horizontal axis is labeled Position, x (m), with major tick marks and numerical labels at -0.60, -0.40, -0.20, 0, 0.20, 0.40, and 0.60. The vertical axis is labeled Energy (J), with major tick marks and numerical labels at 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20. Light gray gridlines extend across the plotting area at every major tick. A solid curve represents the potential energy U(x), forming a symmetric upward-opening parabola with its minimum vertex at (0, 0) and passing through points (-0.60, 18), (-0.40, 8), (-0.20, 2), (0.20, 2), (0.40, 8), and (0.60, 18). A text label U(x) sits adjacent to the curve in the first quadrant. A horizontal dashed line at E = 18 J extends from x = -0.60 to x = 0.60, intersecting the parabola at the turning points, with a label E placed just to the right of x = 0.60. No other labels, curves, shading, or text appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460307-f0c27C.jpg)

- **A.** \(60\text{ m/s}^2\)
- **B.** \(90\text{ m/s}^2\)
- **C.** \(120\text{ m/s}^2\)
- **D.** \(200\text{ m/s}^2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121003/*