---
title: "A block of mass \\(m\\) is attached to an ideal spring of spring constant \\(k\\). In Configuration 1, the block hangs vertically in equilibrium with spring extension \\(\\Delta x_1\\) and oscillates with period \\(T_1\\). In Configuration 2, the identical block and spring are placed on a frictionless ramp inclined at an angle \\(\\theta\\) above the horizontal, where \\(0^\\circ < \\theta < 90^\\circ\\), resting in equilibrium with spring extension \\(\\Delta x_2\\) and oscillating along the ramp with period \\(T_2\\). Which of the following correctly compares the equilibrium extensions and the oscillation periods of the two configurations?"
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/124586/"
date_modified: "2026-09-28T14:08:45+00:00"
---

# A block of mass \(m\) is attached to an ideal spring of spring constant \(k\). In Configuration 1, the block hangs vertically in equilibrium with spring extension \(\Delta x_1\) and oscillates with period \(T_1\). In Configuration 2, the identical block and spring are placed on a frictionless ramp inclined at an angle \(\theta\) above the horizontal, where \(0^\circ < \theta < 90^\circ\), resting in equilibrium with spring extension \(\Delta x_2\) and oscillating along the ramp with period \(T_2\). Which of the following correctly compares the equilibrium extensions and the oscillation periods of the two configurations?

A block of mass \(m\) is attached to an ideal spring of spring constant \(k\). In Configuration 1, the block hangs vertically in equilibrium with spring extension \(\Delta x_1\) and oscillates with period \(T_1\). In Configuration 2, the identical block and spring are placed on a frictionless ramp inclined at an angle \(\theta\) above the horizontal, where \(0^\circ < \theta < 90^\circ\), resting in equilibrium with spring extension \(\Delta x_2\) and oscillating along the ramp with period \(T_2\). Which of the following correctly compares the equilibrium extensions and the oscillation periods of the two configurations?

![A grayscale diagram showing two side-by-side configurations labeled Configuration 1 and Configuration 2. On the left, Configuration 1 shows a horizontal ceiling cross-hatched above, from which a vertical helical spring hangs downward. A square block of mass labeled m is attached to the bottom of the spring. On the right, Configuration 2 shows a right-triangular incline resting on a flat horizontal surface. The incline rises from right to left at an angle labeled \theta relative to the horizontal. A rigid support is perpendicular to the top of the incline. Attached to this support is a helical spring aligned parallel to the incline surface. A square block of mass labeled m is attached to the lower end of this spring, resting on the smooth incline. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604524-oRe4M9.jpg)

- **A.** Equilibrium extension: \(\Delta x_2 = \Delta x_1\) ; Period: \(T_2 > T_1\)
- **B.** Equilibrium extension: \(\Delta x_2 = \Delta x_1\) ; Period: \(T_2 = T_1\)
- **C.** Equilibrium extension: \(\Delta x_2 < \Delta x_1\) ; Period: \(T_2 = T_1\)
- **D.** Equilibrium extension: \(\Delta x_2 < \Delta x_1\) ; Period: \(T_2 > T_1\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124586/*