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Initial mass from the change in period when a known mass is added to a spring

The same question, asked 2 times: 4 May 2023 S2*, 11 May 2024 S2. Every wording below, oldest first.

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  1. Question 1

    4 May 2023 S2

    40
    A mass 'm' attached to a spring oscillates with a period of 3 second. If the mass is increased by 0.6 kg, the period increases by 3 second. The initial mass 'm' is equal to

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  2. Question 2

    11 May 2024 S2

    21
    The upper end of the spring is fixed and a mass 'm' is attached to its lower end. When mass is slightly pulled down and released, it oscillates with time period 3 second. If mass 'm' is increased by 1 kg, the time period becomes 5 second. The value of 'm' is (mass of spring is negligible)

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