---
title: "A block of mass \\(m\\) on a horizontal, frictionless surface is attached to the end of a non-ideal spring. The block is pulled to position \\(x = -x_0\\) and released from rest at time \\(t = 0\\). The graph shows the horizontal force \\(F_x\\) exerted by the spring on the block as a function of the block’s position \\(x\\) between \\(x = -x_0\\) and \\(x = +x_0\\).  Which of the following statements correctly describes the motion of the block?"
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url: "https://nerd-notes.com/ubq/120978/"
date_modified: "2026-08-23T04:44:55+00:00"
---

# A block of mass \(m\) on a horizontal, frictionless surface is attached to the end of a non-ideal spring. The block is pulled to position \(x = -x_0\) and released from rest at time \(t = 0\). The graph shows the horizontal force \(F_x\) exerted by the spring on the block as a function of the block’s position \(x\) between \(x = -x_0\) and \(x = +x_0\).

Which of the following statements correctly describes the motion of the block?

A block of mass \(m\) on a horizontal, frictionless surface is attached to the end of a non-ideal spring. The block is pulled to position \(x = -x_0\) and released from rest at time \(t = 0\). The graph shows the horizontal force \(F_x\) exerted by the spring on the block as a function of the block's position \(x\) between \(x = -x_0\) and \(x = +x_0\).

Which of the following statements correctly describes the motion of the block?

![A 2D Cartesian graph with a horizontal axis labeled x and a vertical axis labeled F_x. The horizontal axis has tick marks labeled -x_0, 0, and x_0. The vertical axis has tick marks labeled -F_0, 0, and F_0. A single solid curve passes continuously through three key points: (-x_0, F_0), (0, 0), and (x_0, -F_0). For x between -x_0 and 0, the curve lies entirely above the horizontal axis, curving downward to pass through the origin. For x between 0 and x_0, the curve lies entirely below the horizontal axis, curving downward to end at (x_0, -F_0). The curve is symmetric under point reflection through the origin. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460294-pyfGu4.jpg)

- **A.** The block undergoes simple harmonic motion because the spring force is directed toward \(x = 0\) for all displacements.
- **B.** The magnitude of the block's acceleration is at a maximum at \(x = 0\) because the magnitude of the slope \(\left|\dfrac{dF_x}{dx}\right|\) is greatest at \(x = 0\).
- **C.** The total mechanical energy of the block-spring system decreases as the block moves from \(x = -x_0\) to \(x = 0\) because the magnitude of the spring force decreases.
- **D.** The kinetic energy of the block at \(x = 0\) is equal to the area bounded by the \(F_x\text{-versus-}x\) curve and the horizontal axis from \(x = -x_0\) to \(x = 0\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120978/*