®¶Àú¡G²¿Ó¹B°Ê¡Bªý¥§»P¦@®¶

 

²¿Ó¹B°Ê

²¿Ó¹B°Êªº©w¸q

x(t) = A0 sin(ωt + φ)

¨ä¤¤

A0 ¬O®¶´T

ω¬O¨¤ÀW²v¡A1/ (2 π ω) = T ¬O¶g´Á

φ¬O¬Û¦ì¨¤

 

½Æ¼Æªºªí¥Üªk¤]«Ü±`¨£

x(t) = A0 ei(ωt + φ)

¨ä¤¤ eiθ = cos(θ) + i sin(θ)

ei(ωt + φ) = cos(ωt + φ) + i sin(ωt + φ)

 

²¿Ó¹B°Êªº­y¸ñ

¤@ºû±¡ªp

 

¨â­Ó¿W¥ß SHG ¹Ï§Î¤§²Õ¦X¡G§õ¨F¨|¹Ï§Î

Ax, Ay, ωx, ωy, δx, δy ¬Ò¤£¦P

 

 

 

 

²¿Ó®¶Àúªº¹B°Ê¤èµ{¦¡

¹ï®É¶¡·L¤À¨â¦¸

 

·L¤À¤èµ{¦¡¡]¹B°Ê¤èµ{¦¡¡^

d2 x(t) /dt2 = - k/m x(t)

¤]´N¬O»¡¡A¸j¦b¡]½è¶q¥i²¤¤£­p¤§¡^¼u®¤W ªºª«Å骺¹B°Ê¦æ¬°¡A¨ä¤¤ ω = √(k/M)

 

¦ì¯à

U = (1/2) ω x2

 

²¿Ó¹B°Ê¤§­«­n©Ê

¥ô¦ó¦^´_¤O¦ì¶Õ¦b±µªñ¥­¿ÅÂI³B³£¬O©ßª«½u§Î¡A¤]´N¬O¤@¦¸¤è¤O¡C¡]¼Æ¾Ç¤W¥iÃÒ©ú¨ç¦b·¥­È³B¥Ñ©ó±×²v¬°¹s¡A®õ°Ç®i¶}¥Ñ¥­¤è¶µ¶}©l¡A¬G¦³¤W­z©Ê½è¡C¡^½Æ²ß¡G®õ°Ç®i¶}¦¡¡C

 

http://mathworld.wolfram.com/TaylorSeries.html

 

 

¦h½èÂI¨t²Î¤§ªº®¶Àúªº°ò¥»¼Ò¦¡¡]Normal Mode¡^

 

ºû°ò¦Ê¬ì http://en.wikipedia.org/wiki/Normal_mode

 

C2H6 ¤À¤l¤§ normal modes ªº¨ä¤¤¤TºØ

 

 

´XºØ±`¨£ªºÂ²¿Ó¹B°Ê¸Ë¸m

¼u®

 

§áÂ\

Fig 15-7

τ = - κ θ

 

²³æÄÁÂ\¡]³æÂ\¡^

 

¯u¹ê¡]ª«²z¡^Â\

¤]¦³Â½Ä¶§@½ÆÂ\

¶g´Á¬O (15-29) ¦¡

¥i§Q¥Î½ÆÂ\¨Óºë±K¶q´ú g ­È

g ­È¬O (15-31) ¦¡¡]³æÂ\¤½¦¡ùتº g ®ø±¼©Ò¥H¤£¯à¨D g¡^

 

§¡¤Ã¡]µ¥³t¡^¶ê©P¹B°Êªº§ë¼v

 

 

 

ªý¥§

ªý¤O

¬O¤@ºØ®ø¯Ó¤O¾Ç¯à¡]¾÷±ñ¯à¡^ªº¹Lµ{¡A»P³t«×¦³Ãö¡A¨Ò¦p¤U¹Ï¸Ë¸m

Fd = - b v

¥N¤J Fnet = m a¡A±o

- b v - k x = m a

¨üªý¥§Â²¿Ó¹B°Ê¤èµ{¦¡ªº¸Ñ

¸Ñ·L¤À¤èµ{¦¡

-bv - k x = ma

m d2 x/dt2 + b dx/dt + kx = 0

³q¸Ñ¬°

x(t) = A0 e -bt/2m cos(ω't + φ)

¦³·sªº¨¤ÀW²v

ω' = ( k/m - b2/4m )(1/2)

¦Ó­«­nªº¬OÀH®É¶¡«ü¼Æ°I´îªº¦]¤l¡A­n®M¦b®¶´T¤W

e -bt/2m A0cos(ω't + φ)

±N³y¦¨ under damping, over damping, critical damping µ¥²{¶H

¥H under dampling §Y b < √(km) ¬°¨Ò

 

¼Æ­Èªº¹q¸£¼ÒÀÀ

¤]¥i¥H«Ü¤è«K¦a¥Î¹q¸£¼ÒÀÀ¥X¨Ó

 

 

¬I¤O®¶Àú »P ¦@®¶

¬I¤O®¶Àú (forcaed oscillation)

¦³¥~¤Oªº

 

Àþ¶¡¥~¤O

¥Î½Ä¶q³B²z¡A´«¦¨ªì³t«×

 

¶g´Á¥~¤O

·íÅX°Ê¤OÀW²v ωd µ¥©ó®¶Àú¨t²Îªº¦ÛµMÀW²v ω ®É¡A®¶´T·|¶V¨Ó¶V¤j¡Cª½¨ì³Qªý¥§©è®ø¦Ó¹F¨ì³Ì¤j­È¡C

 

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