---
title: "A block of mass \\(m_1\\) is placed on top of a second block of mass \\(m_2\\), which is attached to a horizontal ideal spring with spring constant \\(k\\). The lower block slides along a frictionless horizontal surface, and the coefficient of static friction between the two blocks is \\(\\mu_s\\). The system is displaced from its equilibrium position and released from rest to undergo simple harmonic motion. What is the maximum amplitude of oscillation \\(A_{\\max}\\) for which block \\(m_1\\) will oscillate without slipping relative to block \\(m_2\\)?"
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/120972/"
date_modified: "2026-08-23T04:44:53+00:00"
---

# A block of mass \(m_1\) is placed on top of a second block of mass \(m_2\), which is attached to a horizontal ideal spring with spring constant \(k\). The lower block slides along a frictionless horizontal surface, and the coefficient of static friction between the two blocks is \(\mu_s\). The system is displaced from its equilibrium position and released from rest to undergo simple harmonic motion. What is the maximum amplitude of oscillation \(A_{\max}\) for which block \(m_1\) will oscillate without slipping relative to block \(m_2\)?

A block of mass \(m_1\) is placed on top of a second block of mass \(m_2\), which is attached to a horizontal ideal spring with spring constant \(k\). The lower block slides along a frictionless horizontal surface, and the coefficient of static friction between the two blocks is \(\mu_s\). The system is displaced from its equilibrium position and released from rest to undergo simple harmonic motion. What is the maximum amplitude of oscillation \(A_{\max}\) for which block \(m_1\) will oscillate without slipping relative to block \(m_2\)?

![A horizontal line represents a frictionless floor. A vertical hatched wall stands at the left. A horizontal coiled spring labeled k extends from the wall to the left face of a rectangular block labeled m_2 resting on the floor. A smaller rectangular block labeled m_1 sits centered on top of block m_2. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460293-mWlSKl.jpg)

- **A.** \(\dfrac{\mu_s (m_1 + m_2) g}{k}\)
- **B.** \(\dfrac{\mu_s m_1 g}{k}\)
- **C.** \(\dfrac{\mu_s m_2 g}{k}\)
- **D.** \(\dfrac{\mu_s m_1 m_2 g}{(m_1 + m_2) k}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120972/*