---
title: "A student performs an experiment to determine the spring constant \\(k\\) of an ideal spring. The student suspends various masses \\(m\\) from the spring, sets each into small vertical simple harmonic oscillations, and measures the corresponding period \\(T\\). To produce a straight-line graph whose slope is directly equal to \\(k\\), which of the following pairs of quantities should the student plot on the vertical and horizontal axes?"
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url: "https://nerd-notes.com/ubq/120987/"
date_modified: "2026-08-23T04:44:57+00:00"
---

# A student performs an experiment to determine the spring constant \(k\) of an ideal spring. The student suspends various masses \(m\) from the spring, sets each into small vertical simple harmonic oscillations, and measures the corresponding period \(T\). To produce a straight-line graph whose slope is directly equal to \(k\), which of the following pairs of quantities should the student plot on the vertical and horizontal axes?

A student performs an experiment to determine the spring constant \(k\) of an ideal spring. The student suspends various masses \(m\) from the spring, sets each into small vertical simple harmonic oscillations, and measures the corresponding period \(T\). To produce a straight-line graph whose slope is directly equal to \(k\), which of the following pairs of quantities should the student plot on the vertical and horizontal axes?

![A vertical physical setup shown in grayscale. At the top, a horizontal hatched ceiling supports the upper fixed end of a vertical helical spring. The spring hangs downward along a vertical line. Attached to the bottom end of the spring is a rectangular block of mass labeled \(m\). A vertical two-headed arrow is drawn to the right of the block, indicating up-and-down oscillation. A dashed horizontal reference line passes through the center of the block. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460297-BQkkEI.jpg)

- **A.** \(T^2\) on the vertical axis and \(4\pi^2 m\) on the horizontal axis
- **B.** \(2\pi m\) on the vertical axis and \(T^2\) on the horizontal axis
- **C.** \(4\pi^2 m\) on the vertical axis and \(T^2\) on the horizontal axis
- **D.** \(T\) on the vertical axis and \(2\pi\sqrt{m}\) on the horizontal axis

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120987/*