---
title: "A block of mass \\(M\\) on a frictionless horizontal surface is attached to two identical ideal springs, each with spring constant \\(k\\). In Configuration P, the two springs are connected in parallel between the block and a wall. In Configuration S, the two springs are connected in series between the block and the wall. Both systems are displaced from equilibrium and released to undergo simple harmonic motion. Which of the following correctly identifies the effective spring constants \\(k_{\\text{P}}\\) and \\(k_{\\text{S}}\\) and the ratio of their angular frequencies \\(\\dfrac{\\omega_{\\text{P}}}{\\omega_{\\text{S}}}\\)?  | | \\(k_{\\text{P}}\\) | \\(k_{\\text{S}}\\) | \\(\\dfrac{\\omega_{\\text{P}}}{\\omega_{\\text{S}}}\\) | | :— | :—: | :—: | :—: |"
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url: "https://nerd-notes.com/ubq/120999/"
date_modified: "2026-08-23T04:45:05+00:00"
---

# A block of mass \(M\) on a frictionless horizontal surface is attached to two identical ideal springs, each with spring constant \(k\). In Configuration P, the two springs are connected in parallel between the block and a wall. In Configuration S, the two springs are connected in series between the block and the wall. Both systems are displaced from equilibrium and released to undergo simple harmonic motion. Which of the following correctly identifies the effective spring constants \(k_{\text{P}}\) and \(k_{\text{S}}\) and the ratio of their angular frequencies \(\dfrac{\omega_{\text{P}}}{\omega_{\text{S}}}\)?

| | \(k_{\text{P}}\) | \(k_{\text{S}}\) | \(\dfrac{\omega_{\text{P}}}{\omega_{\text{S}}}\) |
| :— | :—: | :—: | :—: |

A block of mass \(M\) on a frictionless horizontal surface is attached to two identical ideal springs, each with spring constant \(k\). In Configuration P, the two springs are connected in parallel between the block and a wall. In Configuration S, the two springs are connected in series between the block and the wall. Both systems are displaced from equilibrium and released to undergo simple harmonic motion. Which of the following correctly identifies the effective spring constants \(k_{\text{P}}\) and \(k_{\text{S}}\) and the ratio of their angular frequencies \(\dfrac{\omega_{\text{P}}}{\omega_{\text{S}}}\)?

| | \(k_{\text{P}}\) | \(k_{\text{S}}\) | \(\dfrac{\omega_{\text{P}}}{\omega_{\text{S}}}\) |
| :--- | :---: | :---: | :---: |

![A schematic diagram showing two separate horizontal spring-mass systems labeled Configuration P and Configuration S, viewed from above on a frictionless surface. In Configuration P at the top, a vertical line on the left represents a fixed wall. Two identical horizontal zig-zag lines representing springs, each labeled \(k\), extend parallel to each other from the wall to the left face of a rectangular block labeled \(M\). In Configuration S at the bottom, a vertical line on the left represents a fixed wall. Two identical zig-zag lines representing springs, each labeled \(k\), are connected end-to-end in a single horizontal line between the wall and the left face of a rectangular block labeled \(M\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460304-O4AboJ.jpg)

- **A.** | \(2k\) | \(\dfrac{k}{2}\) | \(2\) |
- **B.** | \(2k\) | \(\dfrac{k}{2}\) | \(4\) |
- **C.** | \(\dfrac{k}{2}\) | \(2k\) | \(\dfrac{1}{2}\) |
- **D.** | \(2k\) | \(\dfrac{k}{2}\) | \(\dfrac{1}{2}\) |

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120999/*