? 發問於 科學及數學其他 - 科學 · 1 十年前

How to derive the effective mass of spring? include formula.

How to derive the effective mass of spring? include formula.

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    Lv 6
    1 十年前
    最愛解答

    (1)F[spring] = -ky ,where y is the displacement and positive k is known as the stiffness.(Hooke's law)

    (2)F[friction] = -by' ,where positive b is the damping coefficient

    negative signs in equations (1) and (2) reflect the opposite nature of the force.

    (3)my" = -ky -by' + F[external] <--from F=ma, where a=d2y/dt2

    rewrite equation (3), we get F[ext] = my" + by' + ky

    or F[ext] = (inertia)*y" + (damping)*y' + (stiffness)*y

    資料來源: myself
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