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Time period or frequency of a spring-mass system when the mass changes

This type of question, asked 4 times: 24 Jan 2023, 30 Jan 2023, 1 Feb 2024, 9 Apr 2024. All 4 questions below, oldest first.

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  1. Question 1

    24 Jan 2023

    117
    A mass mm attached to free end of a spring executes SHM with a period of 1 s1\text{ }s. If the mass is increased by 3 kg3\text{ }kg the period of oscillation increases by one second, the value of mass mm is kgkg.

  2. Question 2

    30 Jan 2023

    110
    For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is 1 kg1\text{ }kg, the angular frequency is ω1\omega_{1}. When the mass block is 2 kg2\text{ }kg the angular frequency is ω2\omega_{2}. The ratio ω2/ω1\omega_{2}/\omega_{1} is

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  3. Question 3

    1 Feb 2024

    111
    A mass mm is suspended from a spring of negligible mass and the system oscillates with a frequency f1f_{1}. The frequency of oscillations if a mass 9 m9\text{ }m is suspended from the same spring is f2f_{2}. The value of f1f2\frac{f_{1}}{f_{2}} is _______

  4. Question 4

    9 Apr 2024

    112
    A particle of mass 0.50 kg0.50\text{ }kg executes simple harmonic motion under force F=−50(Nm−1)xF = - 50\left( Nm^{- 1} \right)x. The time period of oscillation is x35 s\frac{x}{35}\text{ }s. The value of xx is_______ (Given π=227\pi=\frac{22}{7} )