---
title: "A block of mass \\(M\\) is attached to a uniform ideal spring of force constant \\(k_0\\) and oscillates on a horizontal frictionless surface with frequency \\(f_0\\). The spring is then detached and cut into two identical halves. The same block of mass \\(M\\) is attached to one of these half-springs and set into simple harmonic motion on the same surface. What is the ratio \\(\\dfrac{f_{\\text{new}}}{f_0}\\) of the new frequency of oscillation to the original frequency?"
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/120984/"
date_modified: "2026-08-23T04:44:56+00:00"
---

# A block of mass \(M\) is attached to a uniform ideal spring of force constant \(k_0\) and oscillates on a horizontal frictionless surface with frequency \(f_0\). The spring is then detached and cut into two identical halves. The same block of mass \(M\) is attached to one of these half-springs and set into simple harmonic motion on the same surface. What is the ratio \(\dfrac{f_{\text{new}}}{f_0}\) of the new frequency of oscillation to the original frequency?

A block of mass \(M\) is attached to a uniform ideal spring of force constant \(k_0\) and oscillates on a horizontal frictionless surface with frequency \(f_0\). The spring is then detached and cut into two identical halves. The same block of mass \(M\) is attached to one of these half-springs and set into simple harmonic motion on the same surface. What is the ratio \(\dfrac{f_{\text{new}}}{f_0}\) of the new frequency of oscillation to the original frequency?

![A schematic diagram showing a horizontal frictionless surface represented by a solid horizontal line. On the left, a vertical wall with hatching on its outer side serves as a fixed anchor. A horizontal coil spring labeled \(k_0\) is attached to the vertical wall at its left end and to the left face of a rectangular block labeled \(M\) at its right end. The block rests on the horizontal surface. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460296-eBTpY4.jpg)

- **A.** \(\dfrac{1}{2}\)
- **B.** \(\dfrac{\sqrt{2}}{2}\)
- **C.** \(\sqrt{2}\)
- **D.** \(2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120984/*