A spring stretches by 0.0173 m when a 2.62-kg object is suspended from its end. How much mass should be attached to this spring so that its

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A spring stretches by 0.0173 m when a 2.62-kg object is suspended from its end. How much mass should be attached to this spring so that its frequency of vibration is f = 3.0 Hz?

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  1. Answer

    4.16kg mass should be added

    Explanation:

    Step one :

    Given

    Extention e=0.0173m

    Suspended Mass m=2.62kg

    Frequency f=3hz

    But F=ma

    F=2.62*9.81

    F=25.6N

    Step two

    Applying the hooks law equation

    F=ke

    Where k is the spring constant

    k=F/e

    k=25.6/0.0173

    k=1480N/m

    Step three

    To solve for the additional mass that causes a frequency of vibration of 3hz

    m=k/4*pi²*f²

    Substituting our values into the equation we have

    m=1480/4*3.142²*3²

    m=1480/355.4

    m=4.16kg

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