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【八一征文】美妙的钟摆之舞

热度 59已有 35596 次阅读2012-8-1 05:14 |个人分类:影在趣中|系统分类:【文队】-诗词/书画| 钟摆。舞蹈

还记得力学课学到的“钟摆的周期与摆长的平方根成正比”吗?即钟摆越长,周期越长(即每个来回需要的时间越长)。哈佛大学的学生们用把15个逐渐加长的钟摆排成一列,让他们一起晃动。请看钟摆之舞!
 
 
注:单摆的周期公式是 T=2Π√L/g ,只与摆长和当地的重力加速度有关,与摆长的平方根成正比,与当地重力加速度的平方根成反比。
 
 

What it shows: Fifteen uncoupled simple pendulums of monotonically increasing lengths dance together to produce visual traveling waves, standing waves, beating, and random motion. One might call this kinetic art and the choreography of the dance of the pendulums is stunning! Aliasing and quantum revival can also be shown.

How it works: The period of one complete cycle of the dance is 60 seconds. The length of the longest pendulum has been adjusted so that it executes 51 oscillations in this 60 second period. The length of each successive shorter pendulum is carefully adjusted so that it executes one additional oscillation in this period. Thus, the 15th pendulum (shortest) undergoes 65 oscillations. When all 15 pendulums are started together, they quickly fall out of sync—their relative phases continuously change because of their different periods of oscillation. However, after 60 seconds they will all have executed an integral number of oscillations and be back in sync again at that instant, ready to repeat the dance.

Setting it up: The pendulum waves are best viewed from above or down the length of the apparatus. Video projection is a must for a large lecture hall audience. You can play the video below to see the apparatus in action. One instance of interest to note is at 30 seconds (halfway through the cycle), when half of the pendulums are at one amplitude maximum and the other half are at the opposite amplitude maximum.

Comments: Our apparatus was built from a design published by Richard Berg 1 at the University of Maryland. He claims their version is copied from one at Moscow State University.  Dr. Jiri Drabek at Palacky University in the Czech Republic has informed us that it was originally designed and constructed by Ernst Mach, professor of mathematics in Praha and Vienna around the year 1867.  The demonstration is used in the Czech Republic under the name "Machuv vinostroj" -- the "Wavemachine of Mach."  The apparatus we have was designed and built by Nils Sorensen.

James Flaten and Kevin Parendo2 have mathematically modeled the collective motions of the pendula with a continuous function. The function does not cycle in time and they show that the various patterns arise from aliasing of this function—the patterns are a manifestation of spatial aliasing (as opposed to temporal). Indeed, if you've ever used a digital scope to observe a sinusoidal signal, you have probably seen some of these patterns on the screen when the time scale was not set appropriately.

Here at Harvard, Prof Eric Heller has suggested that the demonstration could be used to simulate quantum revival. So here you have quantum revival versus classical periodicity!

 


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发表评论 评论 (93 个评论)

回复 pengl 2012-8-2 06:02
猪八戒: a mazing world. it is.
it is.
.
回复 在美一方 2012-8-2 06:07
pengl: 有人送,好挑三拣四的。行啊你
还没还没哦,我是把话说前头省的有冤大头去花那冤枉钱不讨好  
回复 pengl 2012-8-2 06:43
在美一方: 还没还没哦,我是把话说前头省的有冤大头去花那冤枉钱不讨好   
  
回复 深海孤帆 2012-8-2 07:17
妙不可言
回复 pengl 2012-8-2 08:26
深海孤帆: 妙不可言
   问好!
回复 路不平 2012-8-2 08:44
pengl: 共振共鸣
体会能量守恒
回复 pengl 2012-8-2 09:22
路不平: 体会能量守恒
   路平守得长
回复 渔夫 2012-8-2 11:50
太好了。美妙的构思
回复 pengl 2012-8-3 00:00
渔夫: 太好了。美妙的构思
可不是吗?
问候!
回复 路不平 2012-8-3 09:09
pengl:    路平守得长
在发呆
回复 pengl 2012-8-3 12:50
路不平: 在发呆
  
回复 brav 2012-8-5 22:59
amazing, the melodies show up when a group of pendulums  is well organized.

all poem's world  from you
回复 pengl 2012-8-7 08:40
brav: amazing, the melodies show up when a group of pendulums  is well organized.

all poem's world  from you
nice to see you.
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