---
title: "A block of mass \\(m\\) on a frictionless horizontal surface is connected to a rigid wall by an ideal spring of spring constant \\(k\\). An external driving force \\(F(t) = F_0 \\cos(\\omega t)\\) is applied to the block, where \\(F_0\\) and \\(\\omega\\) are positive constants. The differential equation governing the motion of the block is \\(m \\dfrac{d^2x}{dt^2} + kx = F_0 \\cos(\\omega t)\\). Assuming a steady-state solution of the form \\(x(t) = A \\cos(\\omega t)\\), where \\(\\omega \\ne \\sqrt{\\dfrac{k}{m}}\\), which of the following expressions represents the steady-state amplitude \\(A\\) of the oscillation?"
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url: "https://nerd-notes.com/ubq/117643/"
date_modified: "2026-08-04T07:49:27+00:00"
---

# A block of mass \(m\) on a frictionless horizontal surface is connected to a rigid wall by an ideal spring of spring constant \(k\). An external driving force \(F(t) = F_0 \cos(\omega t)\) is applied to the block, where \(F_0\) and \(\omega\) are positive constants. The differential equation governing the motion of the block is \(m \dfrac{d^2x}{dt^2} + kx = F_0 \cos(\omega t)\). Assuming a steady-state solution of the form \(x(t) = A \cos(\omega t)\), where \(\omega \ne \sqrt{\dfrac{k}{m}}\), which of the following expressions represents the steady-state amplitude \(A\) of the oscillation?

A block of mass \(m\) on a frictionless horizontal surface is connected to a rigid wall by an ideal spring of spring constant \(k\). An external driving force \(F(t) = F_0 \cos(\omega t)\) is applied to the block, where \(F_0\) and \(\omega\) are positive constants. The differential equation governing the motion of the block is \(m \dfrac{d^2x}{dt^2} + kx = F_0 \cos(\omega t)\). Assuming a steady-state solution of the form \(x(t) = A \cos(\omega t)\), where \(\omega \ne \sqrt{\dfrac{k}{m}}\), which of the following expressions represents the steady-state amplitude \(A\) of the oscillation?

![A block of mass m rests on a horizontal line representing a frictionless surface. A horizontal spring with spring constant k connects the left side of the block to a vertical wall on the left. A horizontal arrow labeled F(t) points to the right from the right side of the block. A horizontal position axis x extends to the right below the surface, with an origin marked x = 0 directly beneath 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-1-1785829766-ip5NsL.jpg)

- **A.** \(A = \dfrac{F_0}{m\omega^2}\)
- **B.** \(A = \dfrac{F_0}{k + m\omega^2}\)
- **C.** \(A = \dfrac{F_0}{|k - m\omega^2|}\)
- **D.** \(A = \dfrac{F_0}{\sqrt{k^2 + m^2\omega^4}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117643/*