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Spring constant when a spring is cut or springs are joined in series

This type of question, asked 3 times: 2021 Paper 25, 24 Jan 2026 S1, 8 Apr 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    2021 Paper 25

    19
    If two similar springs each of spring constant K1K_{1} are joined in series, the new spring constant and time period would be changed by a factor:

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  2. Question 2

    24 Jan 2026 S1

    11
    A spring of force constant 15 N/m15\text{ }N/m is cut into two pieces. If the ratio of their length is 1:31:3, then the force constant of smaller piece is ____\_\_\_\_ N/mN/m

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  3. Question 3

    8 Apr 2026 S2

    12
    The frequency of oscillation of a mass m suspended by spring is v1v_{1}. If the length of the spring is cut to half, the same mass oscillates with frequency v2v_{2}. The value of v2v1\frac{v_{2}}{v_{1}} is ____\_\_\_\_ .

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