A spring oscillator is designed with a mass of 0.223 kg. It operates while immersed in a damping fluid, selected so that the oscillation amp

Question

A spring oscillator is designed with a mass of 0.223 kg. It operates while immersed in a damping fluid, selected so that the oscillation amplitude decreases to 1.00 % of its initial value in 9.07 s. Determine the damping coefficient b of the system.

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Acacia 5 years 2021-07-21T06:14:09+00:00 1 Answers 10 views 0

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  1. kimchi2
    0
    2021-07-21T06:15:38+00:00
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    Answer:

    The damping coefficient of the system is 0.226.

    Explanation:

    Given:

    Mass m = 0.223 kg

    Time t = 9.07 sec

    From the formula of amplitude,

        A = A_{o} e^{-\alpha t }

    Where \alpha = \frac{b}{2m}

    Here amplitude decrease to 1%

    So we write,

       0.01 = e^{-\alpha 9.07 }

    \ln 0.01 = - \alpha 9.07

    -4.605 = - \alpha 9.07

       \alpha = 0.507

    Here \alpha = \frac{b}{2m}

    Where b = damping coefficient

      b = \alpha 2m

      b = 2 \times 0.507 \times 0.223

      b = 0.226

    Therefore, the damping coefficient of the system is 0.226.

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