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

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

### 1 個解答

• 匿名
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&#39;s law)

(2)F[friction] = -by&#39; ,where positive b is the damping coefficient

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

(3)my&quot; = -ky -by&#39; + F[external] &lt;--from F=ma, where a=d2y/dt2

rewrite equation (3), we get F[ext] = my&quot; + by&#39; + ky

or F[ext] = (inertia)*y&quot; + (damping)*y&#39; + (stiffness)*y

資料來源： myself