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Spring constant or amplitude from the energy at a given position

This type of question, asked 3 times: 1 Feb 2023, 13 Apr 2023, 8 Apr 2024. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    1 Feb 2023

    111
    A block is fastened to a horizontal spring. The block is pulled to a distance x=10 cmx = 10\text{ }cm from its equilibrium position (at x=0x = 0 ) on a frictionless surface from rest. The energy of the block at x=5 cmx = 5\text{ }cm is 0.25 J0.25\text{ }J. The spring constant of the spring is ____\_\_\_\_ Nm−1Nm^{- 1}

  2. Question 2

    13 Apr 2023

    23
    At a given point of time the value of displacement of a simple harmonic oscillator is given as y=Acos(30∘)y = Acos\left( 30^{\circ} \right). If amplitude is 40 cm40\text{ }cm and kinetic energy at that time is 200 J200\text{ }J, the value of force constant is 1.0×10xNm−11.0 \times10^{x}Nm^{- 1}. The value of xx is___

  3. Question 3

    8 Apr 2024

    117
    An object of mass 0.2 kg0.2\text{ }kg executes simple harmonic motion along xx axis with frequency of (25π)Hz\left( \frac{25}{\pi} \right)Hz. At the position x=0.04 mx= 0.04\text{ }m the object has kinetic energy 0.5 J0.5\text{ }J and potential energy 0.4 J0.4\text{ }J. The amplitude of oscillation is_____ cmcm.