用户注册 登录
珍珠湾全球网 返回首页

pengl的个人空间 http://bay.zhenzhubay.com/?23 [收藏] [复制] [分享] [RSS]

日志

【八一征文】美妙的钟摆之舞

热度 59已有 19594 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!

 


路过

鸡蛋
50

鲜花
6

支持

雷人

难过

搞笑

刚表态过的朋友 (56 人)

 

发表评论 评论 (93 个评论)

回复 人間的盒子 2012-8-1 05:29
来了
回复 pengl 2012-8-1 05:38
人間的盒子: 来了
请香茶!
回复 張川上 2012-8-1 05:40
又科学又藝術
回复 布衣人 2012-8-1 05:42
太有创意了,科技的东西也充滿艺术性。
回复 yuxin_9605 2012-8-1 05:56
奇妙无穷~   
回复 pengl 2012-8-1 05:58
張川上: 又科学又藝術
是妙不可言,所以赶紧转贴分享。
回复 pengl 2012-8-1 05:59
布衣人: 太有创意了,科技的东西也充滿艺术性。
谁说科学和艺术没有交集?所以赶紧转贴分享。
回复 pengl 2012-8-1 05:59
yuxin_9605: 奇妙无穷~    
科(学)艺(术)合一
回复 丹奇 2012-8-1 06:00
美妙无比!
回复 照偏天地 2012-8-1 06:06
钟摆之舞也真太有趣的
回复 張川上 2012-8-1 06:09
pengl: 是妙不可言,所以赶紧转贴分享。
謝謝啦
回复 pengl 2012-8-1 06:13
丹奇: 美妙无比!
仙丹奇舞!
回复 pengl 2012-8-1 06:14
照偏天地: 钟摆之舞也真太有趣的
是妙趣横生
回复 pengl 2012-8-1 06:14
張川上: 謝謝啦
谢了,川上!
回复 照偏天地 2012-8-1 06:29
pengl: 是妙趣横生
真的真的
回复 ww_719 2012-8-1 06:34
cool~~~~~
回复 伊兰泓 2012-8-1 06:44
奇思妙想啊!
回复 绛紫湮 2012-8-1 06:53
西西 我来拉
回复 在美一方 2012-8-1 06:58
完了晚了
回复 pengl 2012-8-1 07:07
照偏天地: 真的真的
  
12345下一页

facelist

您需要登录后才可以评论 登录 | 用户注册

Archiver|手机版|珍珠湾全球网

GMT+8, 2019-10-18 17:57 , Processed in 0.027204 second(s), 9 queries , Apc On.

Powered by Discuz! X2.5

回顶部