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Two springs with equal masses: ratio of amplitudes or maximum speeds

This type of question, asked 3 times: 2021 Paper 8, 14 Jun 2022, 29 Jan 2025. All 3 questions below, oldest first.

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  1. Question 1

    2021 Paper 8

    14
    Two particles AA and BB of equal masses are suspended from two massless springs of spring constants K1K_{1} and K2K_{2} respectively. If the maximum velocities during oscillations are equal, the ratio of the amplitude of AA and BB is

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  2. Question 2

    14 Jun 2022

    96
    Two massless springs with spring constants 2k2k and 9k9k, carry 50 g50\text{ }g and 100 g100\text{ }g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be:

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  3. Question 3

    29 Jan 2025

    85
    Two bodies A and B of equal mass are suspended from two massless springs of spring constant k1k_{1} and k2k_{2}, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of AA to the maximum velocity of BB is

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