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A mass placed gently on an oscillating block at its mean position: find the new amplitude

The same question, asked 2 times: 2021 Paper 1*, 27 Jul 2022. Every wording below, oldest first.

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  1. Question 1

    2021 Paper 1

    18
    In the given figure, a mass MM is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is kk. The mass oscillates on a frictionless surface with time period TT and amplitude AA. When the mass is in equilibrium position, as shown in the figure, another mass mm is gently fixed upon it. The new amplitude of oscillation will be -

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  2. Question 2

    27 Jul 2022

    27
    A mass 0.9 kg0.9\text{ }kg, attached to a horizontal spring, executes SHM with an amplitude A1A_{1}. When this mass passes through its mean position, then a smaller mass of 124 g124\text{ }g is placed over it and both masses move together with amplitude A2A_{2}. If the ratio A1A2\frac{A_{1}}{A_{2}} is αα−1\frac{\alpha}{\alpha - 1}, then the value of α\alpha will be