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title: "Three independent horizontal mass-spring oscillators, labeled 1, 2, and 3, undergo simple harmonic motion on a frictionless horizontal surface. Oscillator 1 has block mass \\(m_0\\), spring constant \\(k_0\\), and amplitude \\(A_0\\). Oscillator 2 has block mass \\(4m_0\\), spring constant \\(4k_0\\), and amplitude \\(2A_0\\). Oscillator 3 has block mass \\(m_0\\), spring constant \\(4k_0\\), and amplitude \\(A_0\\). Which of the following correctly compares the total mechanical energy \\(E\\), the maximum speed \\(v_{\\max}\\), and the magnitude of maximum acceleration \\(a_{\\max}\\) of the three oscillators?"
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url: "https://nerd-notes.com/ubq/120993/"
date_modified: "2026-08-23T04:45:00+00:00"
---

# Three independent horizontal mass-spring oscillators, labeled 1, 2, and 3, undergo simple harmonic motion on a frictionless horizontal surface. Oscillator 1 has block mass \(m_0\), spring constant \(k_0\), and amplitude \(A_0\). Oscillator 2 has block mass \(4m_0\), spring constant \(4k_0\), and amplitude \(2A_0\). Oscillator 3 has block mass \(m_0\), spring constant \(4k_0\), and amplitude \(A_0\). Which of the following correctly compares the total mechanical energy \(E\), the maximum speed \(v_{\max}\), and the magnitude of maximum acceleration \(a_{\max}\) of the three oscillators?

Three independent horizontal mass-spring oscillators, labeled 1, 2, and 3, undergo simple harmonic motion on a frictionless horizontal surface. Oscillator 1 has block mass \(m_0\), spring constant \(k_0\), and amplitude \(A_0\). Oscillator 2 has block mass \(4m_0\), spring constant \(4k_0\), and amplitude \(2A_0\). Oscillator 3 has block mass \(m_0\), spring constant \(4k_0\), and amplitude \(A_0\). Which of the following correctly compares the total mechanical energy \(E\), the maximum speed \(v_{\max}\), and the magnitude of maximum acceleration \(a_{\max}\) of the three oscillators?

- **A.** Total Energy: \(E_2 > E_3 > E_1\) | Maximum Speed: \((v_{\max,2} = v_{\max,3}) > v_{\max,1}\) | Maximum Acceleration: \(a_{\max,3} > a_{\max,2} > a_{\max,1}\)
- **B.** Total Energy: \(E_2 > E_3 > E_1\) | Maximum Speed: \(v_{\max,2} > v_{\max,3} > v_{\max,1}\) | Maximum Acceleration: \(a_{\max,2} > a_{\max,3} > a_{\max,1}\)
- **C.** Total Energy: \(E_3 > E_2 > E_1\) | Maximum Speed: \(v_{\max,3} > v_{\max,2} > v_{\max,1}\) | Maximum Acceleration: \(a_{\max,3} > a_{\max,2} > a_{\max,1}\)
- **D.** Total Energy: \(E_2 > E_3 > E_1\) | Maximum Speed: \((v_{\max,2} = v_{\max,3}) > v_{\max,1}\) | Maximum Acceleration: \(a_{\max,2} > a_{\max,3} > a_{\max,1}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120993/*