---
title: "A block on a frictionless horizontal surface is attached to an ideal spring and undergoes simple harmonic motion with amplitude \\(A\\). Let \\(x_{\\max}\\) be the maximum displacement, \\(v_{\\max}\\) be the maximum speed, and \\(E\\) be the total mechanical energy of the oscillator. At an instant when the block is at position \\(x = \\dfrac{1}{2}A\\), its speed is \\(v\\) and its kinetic energy is \\(K\\). Which of the following correctly ranks the ratios \\(\\dfrac{|x|}{x_{\\max}}\\), \\(\\dfrac{|v|}{v_{\\max}}\\), and \\(\\dfrac{K}{E}\\) from greatest to least?"
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url: "https://nerd-notes.com/ubq/120959/"
date_modified: "2026-08-23T04:44:43+00:00"
---

# A block on a frictionless horizontal surface is attached to an ideal spring and undergoes simple harmonic motion with amplitude \(A\). Let \(x_{\max}\) be the maximum displacement, \(v_{\max}\) be the maximum speed, and \(E\) be the total mechanical energy of the oscillator. At an instant when the block is at position \(x = \dfrac{1}{2}A\), its speed is \(v\) and its kinetic energy is \(K\). Which of the following correctly ranks the ratios \(\dfrac{|x|}{x_{\max}}\), \(\dfrac{|v|}{v_{\max}}\), and \(\dfrac{K}{E}\) from greatest to least?

A block on a frictionless horizontal surface is attached to an ideal spring and undergoes simple harmonic motion with amplitude \(A\). Let \(x_{\max}\) be the maximum displacement, \(v_{\max}\) be the maximum speed, and \(E\) be the total mechanical energy of the oscillator. At an instant when the block is at position \(x = \dfrac{1}{2}A\), its speed is \(v\) and its kinetic energy is \(K\). Which of the following correctly ranks the ratios \(\dfrac{|x|}{x_{\max}}\), \(\dfrac{|v|}{v_{\max}}\), and \(\dfrac{K}{E}\) from greatest to least?

- **A.** \(\dfrac{K}{E} > \dfrac{|v|}{v_{\max}} > \dfrac{|x|}{x_{\max}}\)
- **B.** \(\dfrac{|v|}{v_{\max}} > \dfrac{K}{E} > \dfrac{|x|}{x_{\max}}\)
- **C.** \(\dfrac{|v|}{v_{\max}} > \dfrac{|x|}{x_{\max}} > \dfrac{K}{E}\)
- **D.** \(\dfrac{K}{E} > \dfrac{|x|}{x_{\max}} > \dfrac{|v|}{v_{\max}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120959/*