---
title: "Two identical blocks, each of mass \\(m\\), rest on a frictionless horizontal surface between two rigid vertical walls.  Block 1 is attached to the left wall by an ideal spring of spring constant \\(k\\), Block 2 is attached to the right wall by an identical spring of spring constant \\(k\\), and the blocks are connected to each other by a central ideal spring of spring constant \\(4k\\).  In Scenario 1, the blocks are released from rest such that their horizontal displacements from equilibrium satisfy \\(x_1(t) = -x_2(t)\\) at all times, whereas in Scenario 2, they are released such that \\(x_1(t) = x_2(t)\\) at all times.  What is the ratio of the angular frequency of oscillation in Scenario 1 to that in Scenario 2, \\(\\dfrac{\\omega_1}{\\omega_2}\\)?"
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url: "https://nerd-notes.com/ubq/124439/"
date_modified: "2026-09-28T14:05:32+00:00"
---

# Two identical blocks, each of mass \(m\), rest on a frictionless horizontal surface between two rigid vertical walls.

Block 1 is attached to the left wall by an ideal spring of spring constant \(k\), Block 2 is attached to the right wall by an identical spring of spring constant \(k\), and the blocks are connected to each other by a central ideal spring of spring constant \(4k\).

In Scenario 1, the blocks are released from rest such that their horizontal displacements from equilibrium satisfy \(x_1(t) = -x_2(t)\) at all times, whereas in Scenario 2, they are released such that \(x_1(t) = x_2(t)\) at all times.

What is the ratio of the angular frequency of oscillation in Scenario 1 to that in Scenario 2, \(\dfrac{\omega_1}{\omega_2}\)?

Two identical blocks, each of mass \(m\), rest on a frictionless horizontal surface between two rigid vertical walls.

Block 1 is attached to the left wall by an ideal spring of spring constant \(k\), Block 2 is attached to the right wall by an identical spring of spring constant \(k\), and the blocks are connected to each other by a central ideal spring of spring constant \(4k\).

In Scenario 1, the blocks are released from rest such that their horizontal displacements from equilibrium satisfy \(x_1(t) = -x_2(t)\) at all times, whereas in Scenario 2, they are released such that \(x_1(t) = x_2(t)\) at all times.

What is the ratio of the angular frequency of oscillation in Scenario 1 to that in Scenario 2, \(\dfrac{\omega_1}{\omega_2}\)?

![A schematic diagram showing a horizontal spring-mass system between two vertical walls. At the far left, a vertical hatched wall is fixed to a horizontal baseline. A horizontal coil spring labeled \(k\) extends to the right from the left wall to the left face of a rectangular block labeled \(m\). From the right face of this first block, a second horizontal coil spring labeled \(4k\) extends to the left face of an identical second rectangular block labeled \(m\). From the right face of the second block, a third horizontal coil spring labeled \(k\) extends to the right to attach to a second vertical hatched wall. Both blocks rest on the flat, horizontal surface represented by a solid horizontal line. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604331-VGu2eb.jpg)

- **A.** \(\sqrt{5}\)
- **B.** \(3\)
- **C.** \(5\)
- **D.** \(9\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124439/*