---
title: "In an experiment to determine the spring constant \\(k\\) of an ideal vertical spring, a student places various known masses \\(m\\) onto a tray of unknown mass \\(m_0\\) attached to the bottom of the spring. The period \\(T\\) of small vertical oscillations is measured for each mass \\(m\\). To obtain a linear relationship that accounts for the unknown mass \\(m_0\\), which quantities should be plotted on the vertical and horizontal axes, and how is \\(k\\) determined from the slope \\(S\\) of the line of best fit?"
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url: "https://nerd-notes.com/ubq/124552/"
date_modified: "2026-09-28T14:08:37+00:00"
---

# In an experiment to determine the spring constant \(k\) of an ideal vertical spring, a student places various known masses \(m\) onto a tray of unknown mass \(m_0\) attached to the bottom of the spring. The period \(T\) of small vertical oscillations is measured for each mass \(m\). To obtain a linear relationship that accounts for the unknown mass \(m_0\), which quantities should be plotted on the vertical and horizontal axes, and how is \(k\) determined from the slope \(S\) of the line of best fit?

In an experiment to determine the spring constant \(k\) of an ideal vertical spring, a student places various known masses \(m\) onto a tray of unknown mass \(m_0\) attached to the bottom of the spring. The period \(T\) of small vertical oscillations is measured for each mass \(m\). To obtain a linear relationship that accounts for the unknown mass \(m_0\), which quantities should be plotted on the vertical and horizontal axes, and how is \(k\) determined from the slope \(S\) of the line of best fit?

![A horizontal hatched line at the top represents a rigid ceiling support. A single vertical coiled spring extends downward from the center of the support. The bottom of the spring attaches to the center of a small horizontal flat tray labeled m_0. A rectangular block labeled m rests on top of the tray. A vertical dashed line with two small arrowheads indicating up-and-down oscillation is positioned to the right of the tray. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604516-1JGy5f.jpg)

- **A.** Vertical axis: \(T\); Horizontal axis: \(m\); with \(k = \dfrac{4\pi^2}{S}\)
- **B.** Vertical axis: \(T\); Horizontal axis: \(\sqrt{m}\); with \(k = \dfrac{4\pi^2}{S^2}\)
- **C.** Vertical axis: \(T^2\); Horizontal axis: \(m\); with \(k = \dfrac{S}{4\pi^2}\)
- **D.** Vertical axis: \(T^2\); Horizontal axis: \(m\); with \(k = \dfrac{4\pi^2}{S}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124552/*