题目内容
一架摆钟,在某地使用时发现,摆长为l1时,每天快t时间;摆长为l2时,每天慢t时间.试分析计算摆长l多大时,这架摆钟才能准确计时.
l=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120601418627.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120601418627.gif)
设一天的时间为t0
摆长为l1时,周期T1=2π
,一天摆动次数为n1=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120601449359.gif)
摆长为l2时,周期T2=2π
,一天摆动次数为n1=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120601449359.gif)
摆长为l时,周期T=2π
,一天摆动的次数n=
,能准确计时.
根据题意可列方程
T(n1-n)=T(n-n2)
经计算,可得准确计时时摆长应为l=
.
摆长为l1时,周期T1=2π
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120601433312.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120601449359.gif)
摆长为l2时,周期T2=2π
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120601480313.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120601449359.gif)
摆长为l时,周期T=2π
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120601605304.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120601449359.gif)
根据题意可列方程
T(n1-n)=T(n-n2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120601698566.gif)
经计算,可得准确计时时摆长应为l=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120601418627.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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