---
title: "A block of mass \\(M = 0.16\\text{ kg}\\) on a frictionless horizontal surface is attached to an ideal spring and oscillates with a period of \\(T_0 = 0.80\\text{ s}\\). As the block passes through its equilibrium position with a speed of \\(v_0 = 1.2\\text{ m/s}\\), a lump of clay of mass \\(m = 0.09\\text{ kg}\\) moving horizontally at \\(v_c = 0.80\\text{ m/s}\\) in the opposite direction collides with and sticks to the block. What is the updated period of oscillation of the block-clay system?"
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url: "https://nerd-notes.com/ubq/124717/"
date_modified: "2026-09-28T14:09:17+00:00"
---

# A block of mass \(M = 0.16\text{ kg}\) on a frictionless horizontal surface is attached to an ideal spring and oscillates with a period of \(T_0 = 0.80\text{ s}\). As the block passes through its equilibrium position with a speed of \(v_0 = 1.2\text{ m/s}\), a lump of clay of mass \(m = 0.09\text{ kg}\) moving horizontally at \(v_c = 0.80\text{ m/s}\) in the opposite direction collides with and sticks to the block. What is the updated period of oscillation of the block-clay system?

A block of mass \(M = 0.16\text{ kg}\) on a frictionless horizontal surface is attached to an ideal spring and oscillates with a period of \(T_0 = 0.80\text{ s}\). As the block passes through its equilibrium position with a speed of \(v_0 = 1.2\text{ m/s}\), a lump of clay of mass \(m = 0.09\text{ kg}\) moving horizontally at \(v_c = 0.80\text{ m/s}\) in the opposite direction collides with and sticks to the block. What is the updated period of oscillation of the block-clay system?

![A schematic diagram showing a horizontal frictionless surface bounded by a vertical wall on the left. An ideal horizontal coiled spring is attached to the wall and extends to the right, connected to a rectangular block labeled M. A horizontal rightward arrow labeled v_0 originates from the center of the block. To the right of the block, a small rounded lump of clay labeled m is shown in midair just above the surface, with a horizontal leftward arrow labeled v_c directed toward the block. A vertical dashed line indicates the equilibrium position of the spring-block system passing through the center of block M. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604557-6vmRjt.jpg)

- **A.** \(0.60\text{ s}\)
- **B.** \(0.64\text{ s}\)
- **C.** \(0.80\text{ s}\)
- **D.** \(1.00\text{ s}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124717/*