---
title: "A block of mass \\(m\\) is placed on a horizontal, frictionless surface and attached to an ideal spring with spring constant \\(k\\). In Experiment 1, the block is pushed to compress the spring a distance \\(d\\) from its equilibrium position and released from rest. In Experiment 2, the same block is pushed to compress the spring a distance \\(2d\\) from its equilibrium position and released from rest. Let \\(K_1\\) be the maximum kinetic energy of the block in Experiment 1 and \\(K_2\\) be the maximum kinetic energy of the block in Experiment 2. Which of the following correctly compares \\(K_2\\) to \\(K_1\\) and provides a valid justification?"
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url: "https://nerd-notes.com/ubq/109315/"
date_modified: "2026-04-10T09:52:22+00:00"
---

# A block of mass \(m\) is placed on a horizontal, frictionless surface and attached to an ideal spring with spring constant \(k\). In Experiment 1, the block is pushed to compress the spring a distance \(d\) from its equilibrium position and released from rest. In Experiment 2, the same block is pushed to compress the spring a distance \(2d\) from its equilibrium position and released from rest. Let \(K_1\) be the maximum kinetic energy of the block in Experiment 1 and \(K_2\) be the maximum kinetic energy of the block in Experiment 2. Which of the following correctly compares \(K_2\) to \(K_1\) and provides a valid justification?

A block of mass \(m\) is placed on a horizontal, frictionless surface and attached to an ideal spring with spring constant \(k\). In Experiment 1, the block is pushed to compress the spring a distance \(d\) from its equilibrium position and released from rest. In Experiment 2, the same block is pushed to compress the spring a distance \(2d\) from its equilibrium position and released from rest. Let \(K_1\) be the maximum kinetic energy of the block in Experiment 1 and \(K_2\) be the maximum kinetic energy of the block in Experiment 2. Which of the following correctly compares \(K_2\) to \(K_1\) and provides a valid justification?

![A horizontal surface with a vertical wall on the left side. A horizontal spring is attached to the wall and connected to a square block of mass m. A vertical dashed line to the right of the block represents the equilibrium position. A second vertical dashed line shows the block shifted to the left, compressing the spring by a distance d.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/ubq-frq-generatedstem-fig-1-1775814742-QbQR31.jpg)

- **A.** \(K_2 = 2K_1\), because the distance the spring is compressed is doubled.
- **B.** \(K_2 = 2K_1\), because the maximum force exerted by the spring on the block is doubled.
- **C.** \(K_2 = 4K_1\), because the initial potential energy of the spring-block system is proportional to the square of the displacement from equilibrium.
- **D.** \(K_2 = 4K_1\), because the maximum acceleration of the block is quadrupled.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109315/*