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Using E = 1/2 k A^2 with the energy at a displacement to find k, amplitude or energy

This type of question, asked 4 times: 9 May 2023 S1, 11 Apr 2026 S2, 13 Apr 2026 S2, 19 May 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    9 May 2023 S1

    6
    In S.H.M. the displacement of a particle at an instant is Y=Acos⁡30∘Y = A\cos 30^\circ, where A=40 cmA = 40\,\text{cm} and kinetic energy is 200 J. If force constant is 1×10x N/m1 \times 10^x\,\text{N/m}, then xx will be [cos⁡30∘=3/2][\cos 30^\circ = \sqrt{3}/2]

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  2. Question 2

    11 Apr 2026 S2

    119
    A mass 0.40.4 kg performs S.H.M. with a frequency 16π\dfrac{16}{\pi} Hz. At a certain displacement it has kinetic energy 22 J and potential energy 1.21.2 J. The amplitude of oscillation is

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  3. Question 3

    13 Apr 2026 S2

    119
    A block is fastened to a horizontal spring. The block is pulled to a distance x=10x = 10 cm from its equilibrium position (at x=0x = 0) on a frictionless surface from rest. The kinetic energy of the block at x=5x = 5 cm is 0.250.25 J. The spring constant of the spring is nearly (in Nm−1\mathrm{Nm^{-1}})

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  4. Question 4

    19 May 2026 S2

    120
    A linear harmonic oscillator of force constant 2×1062 \times 10^6 N/m has amplitude 0.010.01 m. Its

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