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Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決
Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決 
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有關頻率的算式,這是如何算出的?
Dec 25th 2013, 06:30

sqrt(2*7580/0.27)/(2pi)=sqrt(56148)/6.28=236.96/6.28=37.7 

公式推導如下:
您圖片中的 2k 可能是以下的 k (大概是兩個彈簧並聯,或拉兩邊)

角頻率:\omega=2 \pi f.檢視圖片,頻率f為周期T的倒數

其中\omega = \sqrt{\frac{k}{m}}.檢視圖片。推導過程:

   x = A 檢視圖片cos ({ \omega t + \phi })檢視圖片   对于时间t求导,v = - A \omega檢視圖片 sin ({\omega t + \phi}) 檢視圖片   再关于时间t求导a =- A \omega^{2}檢視圖片cos ({ \omega t + \phi })檢視圖片   由牛顿第二定律得a = \frac {F}{m} = \frac {-kx}{m} = \frac {- A cos ({ \omega t + \phi })k}{m}檢視圖片   两式联立得\omega = \sqrt{\frac{k}{m}}.檢視圖片

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