弹簧的固有频率如何计算??

RT要的不是学生解答是工作需要~
2024-12-17 12:54:00
推荐回答(2个)
回答1:

共振频率计算公式为:



“百度知道”里网友给出的公式大多是:



其实,这是共振周期的计算公式,共振周期与共振频率是倒数的关系。即f=1/T


 


我们来核实一下上述公式计算结果的单位就知道了。


以T0共振周期的计算公式为例:m的单位是kg,我们知道,G=mg(G是重力,单位N,m是质量单位kg,g是重力加速度,单位是m/s^2即米每平方秒),所以仅用单位来计算:


m=G/g=N/(m/s^2)=N·s^2/m;k的单位是N/m,所以m/k=(N·s^2/m)/(N/m)==s^2,所以m/k开根号后的单位就是s(秒),乘以常数2π,单位依然是秒。所以是周期(时间单位)


楼上“网友采纳”的结果的公式中,n是随意假设的字母,其实频率一般是用f,周期用T,而式中的n明显代表的是周期,按他的表示,其实频率应该是f=2π*(K/m)^0.5

回答2:

弹簧的固有频率与其所受的边界约束有关,而且与弹簧本身的质量也有关系.而且弹簧有无限多个固有频率.下面给出三种情况下弹簧的固有基频.
1.弹簧两端固定
ν=√(K/m)/2
2.弹簧一端固定一端受谐和力作用
ν=√(K/m)/4
3.弹簧一端固定一端自由
ν=√(K/m)/4

式中K为弹性系数,m为弹簧质量.
其求解过程非常繁杂,要用到高等数学.楼主知道这么多就足够了.

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