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Kinetic and potential energy at a given displacement as fractions of the total energy in SHM

This type of question, asked 7 times: 2021 Paper 7, 2021 Paper 16, 31 Jan 2023, 1 Feb 2023, 12 Apr 2023, 13 Apr 2023, 29 Jan 2024. All 7 questions below, oldest first.

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  1. Question 1

    2021 Paper 7

    13
    For what value of displacement, the kinetic energy and potential energy of a simple harmonic oscillation become equal?

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  2. Question 2

    2021 Paper 16

    1
    Energy of an oscillating system is E. At a particular instant kinetic energy of system is 3E/4. Find displacement of the oscillating particle from its mean position. Its amplitude of oscillation is A.

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  3. Question 3

    31 Jan 2023

    1
    The maximum potential energy of a block executing simple harmonic motion is 25 J25\text{ }J. A is amplitude of oscillation. At A/2A/2, the kinetic energy of the block is:

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  4. Question 4

    1 Feb 2023

    25
    The amplitude of a particle executing SHMSHM is 3 cm3\text{ }cm. The displacement at which its kinetic energy will be 25%25\% more than the potential energy is:___ cmcm.
  5. Question 5

    12 Apr 2023

    14
    A particle is executing Simple Harmonic Motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be:

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  6. Question 6

    13 Apr 2023

    95
    A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is:

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  7. Question 7

    29 Jan 2024

    28
    When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is x8\frac{x}{8}, where x=x = _______