---
title: "An astronaut on a space station uses a Body Mass Measurement Device (BMMD) to determine their mass in microgravity. The device consists of a seat of mass \\(m_s\\) attached to a spring with an unknown spring constant \\(k\\). To calibrate the device, the astronaut attaches several calibration blocks of known mass \\(m\\) to the seat and measures the period of oscillation \\(T\\) for each mass. To determine the spring constant \\(k\\) from a linear graph, which of the following quantities should be plotted on the vertical and horizontal axes, and what is the physical significance of the slope of the resulting best-fit line?"
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url: "https://nerd-notes.com/ubq/112056/"
date_modified: "2026-04-17T19:17:26+00:00"
---

# An astronaut on a space station uses a Body Mass Measurement Device (BMMD) to determine their mass in microgravity. The device consists of a seat of mass \(m_s\) attached to a spring with an unknown spring constant \(k\). To calibrate the device, the astronaut attaches several calibration blocks of known mass \(m\) to the seat and measures the period of oscillation \(T\) for each mass. To determine the spring constant \(k\) from a linear graph, which of the following quantities should be plotted on the vertical and horizontal axes, and what is the physical significance of the slope of the resulting best-fit line?

An astronaut on a space station uses a Body Mass Measurement Device (BMMD) to determine their mass in microgravity. The device consists of a seat of mass \(m_s\) attached to a spring with an unknown spring constant \(k\). To calibrate the device, the astronaut attaches several calibration blocks of known mass \(m\) to the seat and measures the period of oscillation \(T\) for each mass. To determine the spring constant \(k\) from a linear graph, which of the following quantities should be plotted on the vertical and horizontal axes, and what is the physical significance of the slope of the resulting best-fit line?

![A schematic showing a seat of mass m_s attached to a horizontal spring on a frictionless rail. A calibration block of mass m is placed in the seat. An arrow indicates the seat is oscillating back and forth with a period T.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1776453446-j0dD1x.jpg)

- **A.** Vertical axis: \(T\); Horizontal axis: \(m\). The slope is equal to \(\dfrac{2\pi}{\sqrt{k}}\).
- **B.** Vertical axis: \(T^2\); Horizontal axis: \(m\). The slope is equal to \(\dfrac{4\pi^2}{k}\).
- **C.** Vertical axis: \(T^2\); Horizontal axis: \(m\). The slope is equal to \(\dfrac{k}{4\pi^2}\).
- **D.** Vertical axis: \(m\); Horizontal axis: \(T^2\). The slope is equal to \(\dfrac{4\pi^2}{k}\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/112056/*