---
title: "A block of mass \\(m\\) is attached to an ideal horizontal spring of spring constant \\(k\\) and oscillates with amplitude \\(A\\) on a frictionless surface. The kinetic energy \\(K\\) of the block is plotted as a function of the square of its position, \\(x^2\\), as shown in the graph. Which of the following statements correctly identifies the physical meaning of a feature of the graph and its behavior if the spring is replaced with one of spring constant \\(2k\\) while keeping the amplitude \\(A\\) unchanged?"
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url: "https://nerd-notes.com/ubq/124534/"
date_modified: "2026-09-28T14:08:33+00:00"
---

# A block of mass \(m\) is attached to an ideal horizontal spring of spring constant \(k\) and oscillates with amplitude \(A\) on a frictionless surface. The kinetic energy \(K\) of the block is plotted as a function of the square of its position, \(x^2\), as shown in the graph. Which of the following statements correctly identifies the physical meaning of a feature of the graph and its behavior if the spring is replaced with one of spring constant \(2k\) while keeping the amplitude \(A\) unchanged?

A block of mass \(m\) is attached to an ideal horizontal spring of spring constant \(k\) and oscillates with amplitude \(A\) on a frictionless surface. The kinetic energy \(K\) of the block is plotted as a function of the square of its position, \(x^2\), as shown in the graph. Which of the following statements correctly identifies the physical meaning of a feature of the graph and its behavior if the spring is replaced with one of spring constant \(2k\) while keeping the amplitude \(A\) unchanged?

![A Cartesian graph with a horizontal axis and a vertical axis intersecting at an origin labeled 0. The vertical axis is labeled with an uppercase italic K with an arrow pointing upward. The horizontal axis is labeled with an italic lowercase x with a superscript 2, with an arrow pointing to the right. A single straight solid line begins at a point on the vertical axis labeled K_{\text{max}} and slopes linearly downward and to the right, intersecting the horizontal axis at a point labeled x^2_{\text{max}}. The graph contains no gridlines, no data points, and no tick marks. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604513-esTurm.jpg)

- **A.** The slope of the line equals \(-k\), so replacing the spring with one of spring constant \(2k\) doubles the magnitude of the slope and halves the horizontal intercept.
- **B.** The horizontal intercept equals the amplitude \(A\), so replacing the spring with one of spring constant \(2k\) leaves the horizontal intercept unchanged and halves the vertical intercept.
- **C.** The magnitude of the slope equals \(\dfrac{1}{2}k\), so replacing the spring with one of spring constant \(2k\) doubles the vertical intercept and makes the slope twice as steep, leaving the horizontal intercept unchanged.
- **D.** The vertical intercept represents the maximum restoring force \(kA\), so replacing the spring with one of spring constant \(2k\) doubles the vertical intercept while the magnitude of the slope quadruples.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124534/*