---
title: "A block of mass \\(m\\) on a frictionless horizontal surface is attached to an ideal spring. The position of the block as a function of time \\(t\\) is given by \\(x(t) = A \\cos(\\omega t)\\), where \\(A\\) is the amplitude and \\(\\omega\\) is the angular frequency. Which of the following expressions represents the kinetic energy of the block as a function of time \\(t\\)?"
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url: "https://nerd-notes.com/ubq/117571/"
date_modified: "2026-08-04T07:49:09+00:00"
---

# A block of mass \(m\) on a frictionless horizontal surface is attached to an ideal spring. The position of the block as a function of time \(t\) is given by \(x(t) = A \cos(\omega t)\), where \(A\) is the amplitude and \(\omega\) is the angular frequency. Which of the following expressions represents the kinetic energy of the block as a function of time \(t\)?

A block of mass \(m\) on a frictionless horizontal surface is attached to an ideal spring. The position of the block as a function of time \(t\) is given by \(x(t) = A \cos(\omega t)\), where \(A\) is the amplitude and \(\omega\) is the angular frequency. Which of the following expressions represents the kinetic energy of the block as a function of time \(t\)?

- **A.** \(\dfrac{1}{2} m \omega A^2 \sin^2(\omega t)\)
- **B.** \(\dfrac{1}{2} m \omega^2 A^2 \cos^2(\omega t)\)
- **C.** \(\dfrac{1}{2} m \omega^2 A \sin^2(\omega t)\)
- **D.** \(\dfrac{1}{2} m \omega^2 A^2 \sin^2(\omega t)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117571/*