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Time period of a block attached to two springs

This type of question, asked 5 times: 2021 Paper 2, 2021 Paper 4, 24 Jan 2023, 31 Jan 2023, 6 Apr 2023. All 5 questions below, oldest first.

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  1. Question 1

    2021 Paper 2

    14
    In the given figure, a body of mass MM is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant kk, the frequency of oscillation of given body is:

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  2. Question 2

    2021 Paper 4

    3
    Two identical spring of spring constant ' 2 K2\text{ }K ' are attached to a block of mass mm and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. Then time period of oscillations of this system is:

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  3. Question 3

    24 Jan 2023

    27
    A block of a mass 2 kg2\text{ }kg is attached with two identical springs of spring constant 20 N/m20\text{ }N/m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is πx\frac{\pi}{\sqrt{x}} in SI unit. The value of xx is
  4. Question 4

    31 Jan 2023

    24
    In the figure given below, a block of mass M=490 gM = 490\text{ }g placed on a frictionless table is connected with two springs having same spring constant (K=2 N m−1)\left( K = 2\text{ }N{\text{ }m}^{- 1} \right). If the block is horizontally displaced through ' XX ' mm then the number of complete oscillations it will make in 14π14\pi seconds will be___
  5. Question 5

    6 Apr 2023

    18
    A mass mm is attached to two springs as shown in figure. The spring constants of two springs are K1K_{1} and K2K_{2}. For the frictionless surface, the time period of oscillation of mass mm is

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