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Object on a vertically oscillating platform or piston leaving the surface

This type of question, asked 2 times: 15 May 2023 S1, 14 May 2024 S2. All 2 questions below, oldest first.

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  1. Question 1

    15 May 2023 S1

    25
    A horizontal platform with a small object placed on it executes a linear S.H.M. in the vertical direction. The amplitude of oscillation is 40 cm. What should be the least period of these oscillations, so that the object is not detached from the platform? [Take g=10g = 10 m/s2^{2} ]

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  2. Question 2

    14 May 2024 S2

    37
    A block of mass M rests on a piston executing S.H.M. of period one second. The amplitude of oscillations so that the mass is separated from the piston is (g=10 ms−2g = 10\,\text{ms}^{-2}, π2=10\pi^2 = 10)

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