---
title: "An object attached to a horizontal spring oscillates in simple harmonic motion along the \\(x\\)-axis. The position \\(x\\) of the object as a function of time \\(t\\) is shown in the graph below for one complete oscillation of period \\(T\\).  Which of the following graphs best represents the velocity \\(v\\) of the object as a function of time \\(t\\) over the same time interval?"
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url: "https://nerd-notes.com/ubq/121026/"
date_modified: "2026-08-23T04:45:29+00:00"
---

# An object attached to a horizontal spring oscillates in simple harmonic motion along the \(x\)-axis. The position \(x\) of the object as a function of time \(t\) is shown in the graph below for one complete oscillation of period \(T\).

Which of the following graphs best represents the velocity \(v\) of the object as a function of time \(t\) over the same time interval?

An object attached to a horizontal spring oscillates in simple harmonic motion along the \(x\)-axis. The position \(x\) of the object as a function of time \(t\) is shown in the graph below for one complete oscillation of period \(T\).

Which of the following graphs best represents the velocity \(v\) of the object as a function of time \(t\) over the same time interval?

![A two-dimensional Cartesian graph of position \(x\) on the vertical axis versus time \(t\) on the horizontal axis. The horizontal axis extends from \(0\) to \(T\) with tick marks labeled \(0\), \(\dfrac{T}{4}\), \(\dfrac{T}{2}\), \(\dfrac{3T}{4}\), and \(T\). The vertical axis is centered at zero, with tick marks labeled \(+x_{\max}\), \(0\), and \(-x_{\max}\). A single solid sinusoidal curve begins at the origin \((0,0)\), slopes downward into negative values to reach a local minimum at \(\left(\dfrac{T}{4}, -x_{\max}\right)\), rises through the horizontal axis at \(\left(\dfrac{T}{2}, 0\right)\), reaches a local maximum at \(\left(\dfrac{3T}{4}, +x_{\max}\right)\), and descends to cross the horizontal axis at \((T, 0)\). Thin dashed reference lines connect each extremum to its corresponding horizontal and vertical axis tick marks. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-graph-xt-1787460328-pnI0R0.jpg)

- **A.** Graph A
- **B.** Graph B
- **C.** Graph C
- **D.** Graph D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121026/*