---
title: "A student conducts an experiment with an ideal horizontal spring fixed at one end. In the first trial, the student compresses the spring a distance \\(d\\) from its equilibrium position. In the second trial, the student compresses the same spring a distance \\(2d\\) from its equilibrium position. Which of the following correctly compares the elastic potential energy stored in the spring during the second trial to the energy stored during the first trial?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/109178/"
date_modified: "2026-03-21T04:33:40+00:00"
---

# A student conducts an experiment with an ideal horizontal spring fixed at one end. In the first trial, the student compresses the spring a distance \(d\) from its equilibrium position. In the second trial, the student compresses the same spring a distance \(2d\) from its equilibrium position. Which of the following correctly compares the elastic potential energy stored in the spring during the second trial to the energy stored during the first trial?

A student conducts an experiment with an ideal horizontal spring fixed at one end. In the first trial, the student compresses the spring a distance \(d\) from its equilibrium position. In the second trial, the student compresses the same spring a distance \(2d\) from its equilibrium position. Which of the following correctly compares the elastic potential energy stored in the spring during the second trial to the energy stored during the first trial?

![Three horizontal views of the same spring. Top: The spring is at its equilibrium length with its right end at position zero. Middle: The spring is compressed to the left such that its right end is at a distance d from zero. Bottom: The spring is compressed further to the left such that its right end is at a distance 2d from zero. A wall on the left side of each view anchors the spring.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774067620-MV93cm.jpg)

- **A.** The stored energy is 2 times as great because the restoring force exerted by the spring is linearly proportional to the displacement.
- **B.** The stored energy is 4 times as great because the work done to compress the spring is proportional to the square of the displacement.
- **C.** The stored energy is 4 times as great because the spring constant \(k\) doubles when the displacement from equilibrium is doubled.
- **D.** The stored energy is 8 times as great because the energy required to compress a 3-dimensional object is proportional to the cube of the displacement.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109178/*