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title: "A block of mass \\(m\\) is attached to an ideal horizontal spring with spring constant \\(k\\) on a frictionless surface and oscillates in simple harmonic motion with amplitude \\(A\\), period \\(T_0\\), and maximum acceleration \\(a_{\\text{max}, 0}\\). The system is modified by replacing the block with one of mass \\(2m\\) and the spring with one of spring constant \\(4k\\), while maintaining the same oscillation amplitude \\(A\\). Which of the following correctly relates the new period of oscillation \\(T\\) and new maximum acceleration \\(a_{\\text{max}}\\) to their initial values?"
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url: "https://nerd-notes.com/ubq/122218/"
date_modified: "2026-09-27T13:13:40+00:00"
---

# A block of mass \(m\) is attached to an ideal horizontal spring with spring constant \(k\) on a frictionless surface and oscillates in simple harmonic motion with amplitude \(A\), period \(T_0\), and maximum acceleration \(a_{\text{max}, 0}\). The system is modified by replacing the block with one of mass \(2m\) and the spring with one of spring constant \(4k\), while maintaining the same oscillation amplitude \(A\). Which of the following correctly relates the new period of oscillation \(T\) and new maximum acceleration \(a_{\text{max}}\) to their initial values?

A block of mass \(m\) is attached to an ideal horizontal spring with spring constant \(k\) on a frictionless surface and oscillates in simple harmonic motion with amplitude \(A\), period \(T_0\), and maximum acceleration \(a_{\text{max}, 0}\). The system is modified by replacing the block with one of mass \(2m\) and the spring with one of spring constant \(4k\), while maintaining the same oscillation amplitude \(A\). Which of the following correctly relates the new period of oscillation \(T\) and new maximum acceleration \(a_{\text{max}}\) to their initial values?

![A line drawing showing a horizontal mass-spring oscillator on a smooth horizontal ground line. On the left, a vertical wall with hatching on its left side is shown. Attached to the right face of the vertical wall is a horizontal coiled spring with seven coils extending to the right. The right end of the spring is attached to the left face of a rectangular block labeled \(m\). A horizontal dashed line extends below the block, with a short vertical tick mark labeled \(x = 0\) directly below the center of the block. A horizontal arrow points to the right from the vertical tick mark to a point labeled \(+A\). The spring is shown slightly stretched. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790514820-0qyaWA.jpg)

- **A.** \(T = \sqrt{2}\,T_0\) and \(a_{\text{max}} = 2a_{\text{max}, 0}\)
- **B.** \(T = \dfrac{T_0}{\sqrt{2}}\) and \(a_{\text{max}} = 4a_{\text{max}, 0}\)
- **C.** \(T = \dfrac{T_0}{\sqrt{2}}\) and \(a_{\text{max}} = 2a_{\text{max}, 0}\)
- **D.** \(T = \dfrac{T_0}{2}\) and \(a_{\text{max}} = 4a_{\text{max}, 0}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/122218/*