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19 May, 14:49

At what time t1 does the block come back to its original equilibrium position (x=0) for the first time? Express your answer in terms of some or all of the variables: A, k, and m.

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  1. 19 May, 14:59
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    t_1 = 0.5*pi*sqrt (m / k)

    Explanation:

    Given:

    - The block of mass m undergoes simple harmonic motion. With the displacement of x from mean position is given by:

    x (t) = A*cos (w*t)

    Find:

    - At what time t1 does the block come back to its original equilibrium position (x=0) for the first time?

    Solution:

    - The first time the block moves from maximum position to its mean position constitutes of 1/4 th of one complete cycle. So, the required time t_1 is:

    t_1 = 0.25*T

    - Where, T : Time period of SHM.

    - The time period for SHM is given by:

    T = 2*pi*sqrt (m / k)

    Hence,

    t_1 = 0.25 * 2 * pi * sqrt (m / k)

    t_1 = 0.5*pi * sqrt (m / k)
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