---
title: "A block of mass \\(m\\) rests on a frictionless horizontal floor between two fixed vertical walls separated by a distance \\(D\\).  The block is attached to the left wall by an ideal spring with spring constant \\(k_1\\) and unstretched length \\(L_1\\), and to the right wall by an ideal spring with spring constant \\(k_2\\) and unstretched length \\(L_2\\), where \\(D > L_1 + L_2\\).  A coordinate system is defined along the line of motion with the origin \\(x = 0\\) at the left wall and the positive \\(x\\)-axis directed toward the right wall.  Which of the following differential equations correctly describes the position \\(x(t)\\) of the block?"
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url: "https://nerd-notes.com/ubq/124705/"
date_modified: "2026-09-28T14:09:11+00:00"
---

# A block of mass \(m\) rests on a frictionless horizontal floor between two fixed vertical walls separated by a distance \(D\).

The block is attached to the left wall by an ideal spring with spring constant \(k_1\) and unstretched length \(L_1\), and to the right wall by an ideal spring with spring constant \(k_2\) and unstretched length \(L_2\), where \(D > L_1 + L_2\).

A coordinate system is defined along the line of motion with the origin \(x = 0\) at the left wall and the positive \(x\)-axis directed toward the right wall.

Which of the following differential equations correctly describes the position \(x(t)\) of the block?

A block of mass \(m\) rests on a frictionless horizontal floor between two fixed vertical walls separated by a distance \(D\).

The block is attached to the left wall by an ideal spring with spring constant \(k_1\) and unstretched length \(L_1\), and to the right wall by an ideal spring with spring constant \(k_2\) and unstretched length \(L_2\), where \(D > L_1 + L_2\).

A coordinate system is defined along the line of motion with the origin \(x = 0\) at the left wall and the positive \(x\)-axis directed toward the right wall.

Which of the following differential equations correctly describes the position \(x(t)\) of the block?

![A side-view schematic showing a horizontal line representing a frictionless floor bounded by two vertical hatched walls on the left and right, separated by a horizontal distance labeled \(D\). Between the walls rests a rectangular block labeled \(m\). Attached to the left wall and the left face of the block is a horizontal zigzag line representing a spring labeled \(k_1, L_1\). Attached to the right face of the block and the right wall is a second horizontal zigzag line representing a spring labeled \(k_2, L_2\). Below the floor, a horizontal coordinate axis points to the right with an arrowhead labeled \(x\); a vertical tick mark aligned with the inner face of the left wall is labeled \(0\), and a vertical dashed line extends downward from the center of the block to mark its position coordinate \(x\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604551-bxpbE5.jpg)

- **A.** \(\dfrac{d^2x}{dt^2} + \left(\dfrac{k_1 - k_2}{m}\right)x = \dfrac{k_1 L_1 - k_2(D - L_2)}{m}\)
- **B.** \(\dfrac{d^2x}{dt^2} + \left(\dfrac{k_1 + k_2}{m}\right)x = \dfrac{k_1 L_1 + k_2(D - L_2)}{m}\)
- **C.** \(\dfrac{d^2x}{dt^2} + \left(\dfrac{k_1 + k_2}{m}\right)x = \dfrac{k_1 L_1 - k_2(D - L_2)}{m}\)
- **D.** \(\dfrac{d^2x}{dt^2} + \left(\dfrac{k_1 k_2}{m(k_1 + k_2)}\right)x = \dfrac{k_1 k_2(D - L_1 - L_2)}{m(k_1 + k_2)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124705/*