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Period from the static extension of a spring

This type of question, asked 3 times: 13 May 2024 S2, 19 Apr 2025 S2, 12 May 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    13 May 2024 S2

    25
    A mass 'MM' is suspended from a light spring. An additional mass M1M_1 added extends the spring further by a distance 'xx'. Now the combined mass will oscillate on the spring with period T=T=

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  2. Question 2

    19 Apr 2025 S2

    9
    A vertical spring oscillates with period 6 second with mass mm is suspended from it. When the mass is at rest, the spring is stretched through a distance of (Take, acceleration due to gravity, g=π2=10 m/s2g =\pi^{2}= 10\text{ }m/s^{2} )

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  3. Question 3

    12 May 2026 S2

    118
    A spring produces extension ′x′'x' by applying a force ′F′'F' N. A body of mass ′m′'m' suspended from spring oscillates vertically with period ′T′'T'. The mass of the suspended body is (Neglect mass of spring)

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