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Displacement at which kinetic and potential energy are in a given ratio, or the ratio at a given displacement

This type of question, asked 10 times: 9 May 2024 S2, 10 May 2024 S1, 11 May 2024 S1, 22 Apr 2025 S1, 23 Apr 2025 S1, 13 Apr 2026 S2, 16 Apr 2026 S2, 17 Apr 2026 S1, 17 Apr 2026 S2, 20 Apr 2026 S2. All 10 questions below, oldest first.

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  1. Question 1

    9 May 2024 S2

    42
    A particle is vibrating in S.H.M. with an amplitude of 4 cm. At what displacement from the equilibrium position is its energy half potential and half kinetic?

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  2. Question 2

    10 May 2024 S1

    3
    The amplitude of a particle executing S.H.M. is 3 cm. The displacement at which its kinetic energy will be 25% more than the potential energy is

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  3. Question 3

    11 May 2024 S1

    4
    For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at certain displacement xx from the mean position. If AA is the amplitude of S.H.M the value of xx is

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  4. Question 4

    22 Apr 2025 S1

    45
    For a particle performing S.H.M., the total energy is ' nn ' times the kinetic energy, when the displacement of a particle from mean position is 32 A\frac{\sqrt{3}}{2}\text{ }A, where A is the amplitude of S.H.M. The value of ' nn ' is

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  5. Question 5

    23 Apr 2025 S1

    31
    A particle is executing linear S.H.M. starting from mean position. The ratio of the kinetic energy to the potential energy of the particle at a point of half the amplitude is

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  6. Question 6

    13 Apr 2026 S2

    120
    The amplitude of a particle executing SHM is 33 cm. The displacement at which its kinetic energy will be 25%25\% more than the potential energy is (in cm)

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  7. Question 7

    16 Apr 2026 S2

    119
    The maximum potential energy of a block executing S.H.M. is E and amplitude of oscillation is 'A'. The kinetic energy of the block at amplitude A/2 is

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  8. Question 8

    17 Apr 2026 S1

    119
    For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at a certain displacement 'xx' from the mean position. If 'AA' is the amplitude of S.H.M., the value of 'xx' is

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  9. Question 9

    17 Apr 2026 S2

    120
    For a particle performing linear S.H.M. of amplitude 'r', the potential energy is 'λ\lambda' times its total energy. The displacement of particle is

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  10. Question 10

    20 Apr 2026 S2

    119
    For a particle executing S.H.M., the potential energy is nn times the kinetic energy when its displacement from mean position is (223)A\left(\dfrac{2\sqrt{2}}{3}\right)A, where AA is the amplitude of S.H.M. The value of nn is

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