---
title: "A block of mass \\(m\\) is placed on top of a cart of mass \\(M\\). The cart is connected to an ideal horizontal spring with spring constant \\(k\\) and rests on a horizontal surface with negligible friction. The coefficient of static friction between the block and the cart is \\(\\mu_s\\). The system is displaced from equilibrium and released from rest to oscillate in simple harmonic motion. What is the maximum amplitude of oscillation \\(A_{\\text{max}}\\) for which the block will not slip on the cart, in terms of \\(m\\), \\(M\\), \\(k\\), \\(\\mu_s\\), and fundamental constants?"
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/122804/"
date_modified: "2026-09-28T11:02:58+00:00"
---

# A block of mass \(m\) is placed on top of a cart of mass \(M\). The cart is connected to an ideal horizontal spring with spring constant \(k\) and rests on a horizontal surface with negligible friction. The coefficient of static friction between the block and the cart is \(\mu_s\). The system is displaced from equilibrium and released from rest to oscillate in simple harmonic motion. What is the maximum amplitude of oscillation \(A_{\text{max}}\) for which the block will not slip on the cart, in terms of \(m\), \(M\), \(k\), \(\mu_s\), and fundamental constants?

A block of mass \(m\) is placed on top of a cart of mass \(M\). The cart is connected to an ideal horizontal spring with spring constant \(k\) and rests on a horizontal surface with negligible friction. The coefficient of static friction between the block and the cart is \(\mu_s\). The system is displaced from equilibrium and released from rest to oscillate in simple harmonic motion. What is the maximum amplitude of oscillation \(A_{\text{max}}\) for which the block will not slip on the cart, in terms of \(m\), \(M\), \(k\), \(\mu_s\), and fundamental constants?

![A horizontal baseline represents a frictionless surface. At the left end of the baseline, a vertical boundary wall is anchored. A horizontal coiled spring labeled \(k\) extends horizontally to the right from the wall and connects to the left side of a wide rectangular block labeled \(M\). Resting symmetrically on the top flat surface of block \(M\) is a smaller rectangular block labeled \(m\). The contact interface between block \(m\) and block \(M\) is horizontal. A single dashed vertical reference line extends through the center of block \(M\) to denote the equilibrium position. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790593377-LS1YDc.jpg)

- **A.** \(\dfrac{\mu_s m g}{k}\)
- **B.** \(\dfrac{\mu_s M g}{k}\)
- **C.** \(\dfrac{\mu_s (M+m) g}{k}\)
- **D.** \(\dfrac{\mu_s (M+m)^2 g}{M k}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/122804/*