---
title: "A block of mass \\(m\\) on a horizontal frictionless surface is connected to an ideal spring of spring constant \\(k\\). The entire apparatus is immersed in a viscous fluid that exerts a resistive drag force \\(\\vec{F}_d = -b\\vec{v}\\), where the damping constant satisfies \\(b > 2\\sqrt{mk}\\). The block is displaced to position \\(x = +x_0\\) and released from rest at time \\(t = 0\\). Which of the following best describes the qualitative graph of the block’s position \\(x\\) as a function of time \\(t\\)?"
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url: "https://nerd-notes.com/ubq/120550/"
date_modified: "2026-08-23T04:41:33+00:00"
---

# A block of mass \(m\) on a horizontal frictionless surface is connected to an ideal spring of spring constant \(k\). The entire apparatus is immersed in a viscous fluid that exerts a resistive drag force \(\vec{F}_d = -b\vec{v}\), where the damping constant satisfies \(b > 2\sqrt{mk}\). The block is displaced to position \(x = +x_0\) and released from rest at time \(t = 0\). Which of the following best describes the qualitative graph of the block’s position \(x\) as a function of time \(t\)?

A block of mass \(m\) on a horizontal frictionless surface is connected to an ideal spring of spring constant \(k\). The entire apparatus is immersed in a viscous fluid that exerts a resistive drag force \(\vec{F}_d = -b\vec{v}\), where the damping constant satisfies \(b > 2\sqrt{mk}\). The block is displaced to position \(x = +x_0\) and released from rest at time \(t = 0\). Which of the following best describes the qualitative graph of the block's position \(x\) as a function of time \(t\)?

- **A.** A curve that begins at \(x = x_0\) with a negative initial slope and decays toward \(x = 0\), crossing the time axis once before asymptotically approaching zero from below.
- **B.** A sinusoidal curve with an exponentially decaying envelope that begins at \(x = x_0\) with zero initial slope and crosses the time axis repeatedly at fixed intervals.
- **C.** A smooth curve that begins at \(x = x_0\) with zero initial slope, decreases monotonically, and asymptotically approaches \(x = 0\) without crossing the time axis.
- **D.** A curve that begins at \(x = x_0\) with zero initial slope, decreases at an increasing rate until reaching \(x = 0\) at a finite time, and remains at zero thereafter.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120550/*