¹ÌÌåÎïÀíÏ°ÌâÏê½â

ΪÇó¸ñ²¨½â£¬Áî

qai[(2n)??t]?2?x2n?Ae?qai[(2n?1)??t]2?x?2n?1?Be ¡­¡­¡­¡­¡­£¨3£©

½«£¨3£©Ê½´úÈ루2£©Ê½£¬¿Éµ¼³öÏßÐÔ·½³Ì×éΪ

?1?11?12(??)A?(10eiqa/2?e?iqa/2)B?0?mm??11?1??1(eiqa/2?10e?iqa/2)A?(??2)B?0m ?m ¡­¡­¡­¡­¡­£¨4£©

?1Áîm2??0£¬´ÓA£¬BÓзÇÁã½âµÄϵÊýÐÐÁÐʽµÈÓÚÁãµÄÌõ¼þ¿ÉµÃ

2224iqa/2?iqa/2iqa/2?iqa/2(11???)??(10e?e)(e?10e)?0 ¡­¡­00 £¨5£©

22???(11?20cosqa?101) 0ÓÉ£¨5£©Ê½¿É½â³ö

??µ±q?0ʱ£¬cosqa?1£¬?q?µ±

22?0£¬???0

?aʱ£¬cosqa??1£¬???20?0£¬???2?0

ÆäÉ«É¢¹ØϵÇúÏßÈçÏÂͼ3.4Ëùʾ£º

ͼ3.4 Ô­×Ó¼äµÄÁ¦³£Êý²»ÏàµÈµÄË«Ô­×ÓÁ´µÄ¾§¸ñÕñ¶¯É«É¢¹ØϵÇúÏß

12.ÈçÓÐһά²¼À®·Æ¸ñ×Ó£¬µÚ2n¸öÔ­×ÓÓëµÚ2n?1¸öÔ­×ÓÖ®¼äµÄÁ¦³£ÊýΪ?£»¶øµÚ2n¸öÔ­×ÓÓëµÚ2n?1¸öÔ­×ÓµÄÁ¦³£ÊýΪ?'¡£ £¨1£© д³öÕâ¸ö¸ñ×ÓÕñ¶¯µÄ¶¯Á¦Ñ§·½³Ì£» £¨2£© ˵Ã÷ÕâÖÖÇé¿öÒ²ÓÐÉùѧ²¨ºÍ¹âѧ²¨£» £¨3£© Çóq?0ʱ£¬Éùѧ²¨ºÍ¹âѧ²¨µÄƵÂÊ£»

q??£¨4£© Çó

?2a£¨aΪ¾§¸ñ³£Êý£©Ê±£¬Éùѧ²¨ºÍ¹âѧ²¨µÄƵÂÊ¡£

½â£º£¨1£©´ËÌâÓ루11£©Ìâ»ù±¾ÏàËÆ£¬ÔÚ×î½üÁÚ½üËƺͼòг½üËÆÏ£¬Í¬Ñù¿ÉÒÔд³öµÚ2nºÍµÚ2n?1¸öÔ­×ӵĶ¯Á¦Ñ§·½³ÌΪ

21

?d2x2nm??(x2n?1?x2n)??'(x2n?x2n?1)??dt2?2d?mx2n?1??'(x2n?2?x2n?1)??(x2n?1?x2n)2?dt? ¡­¡­¡­¡­¡­£¨1£©

£¨2£©ÎªÇó³ö·½³Ì×飨1£©µÄ¸ñ²¨½â£¬¿ÉÁî

?x2n?Aei[(2n)qa??t]?i[(2n?1)qa??t]x?Be2n?1? ¡­¡­¡­¡­¡­£¨2£©

ÓÚÊǽ«£¨2£©Ê½´úÈ루1£©Ê½£¬¿Éµ¼³öÏßÐÔ·½³Ì×éΪ

?iqa?'?iqa????'2(??)A?(e?e)B?0?mmm??'????'??(eiqa?e?iqa)A?(??2)B?0mm ?m ¡­¡­¡­¡­¡­£¨3£©

???'ÁîµÃ

2224422(???)?(????2??2cos2qa)?0 ¡­¡­¡­¡­¡­0121 £¨4£©

m2??0?£¬m??12?'£¬m2??2´ÓA¡¢BÓзÇÁã½âµÄϵÊýÐÐÁÐʽµÈÓÚÁãµÄÌõ¼þ¿É

ÓÉ£¨4£©Ê½¿É½â³ö

42?2??02??14??2?2?12?2cos2qa ¡­¡­¡­¡­¡­£¨5£©

ÓÉ´Ë¿ÉÖª£¬?µÄÈ¡ÖµÒ²ÓÐ??ºÍ??Ö®·Ö£¬¼´´æÔÚÉùѧ²¨ºÍ¹âѧ²¨ £¨3£©ÓÉ£¨5£©Ê½¿ÉÖª

µ±q?0ʱ£¬cos2qa?1£¬ÓÐ Éùѧ²¨ÆµÂÊ

2????02?(?12??2)£¬¹âѧ²¨ÆµÂÊ

2????02?(?12??2)

£¨4£©Í¬ÑùÓÉ£¨5£©Ê½¿ÉÖª

q??µ±

?2aʱ£¬cos2qa??1£¬ÓÐ

22????0??12??2Éùѧ²¨ÆµÂÊ£¬¹âѧ²¨ÆµÂÊ

22????0??12??2

13.ÔÚһά˫ԭ×ÓÁ´ÖУ¬ÈçM/m??1£¬

£¨1£©ÇóÖ¤£º

?1?2?sinqa?2?M£» 2?m(1?cos2qa)2mM¡£

1q£¨2£©»­³ö?ÓëµÄ¹Øϵͼ£¨ÉèM/m?10£©¡£

22

½â£º£¨1£©ÔÚһά˫ԭ×ÓÁ´ÖУ¬ÆäµÚ2n¸öÔ­×ÓÓëµÚ2n?1¸öÔ­×ÓµÄÔ˶¯·½³ÌΪ

?d2x2nm??(x2n?1?x2n?1?2x2n)??dt2?2?Mdx2n?1??(x?x2n2n?2?2x2n?1)2?dt? ¡­¡­¡­¡­¡­¡­¡­£¨1£©

?x2n?Aei[(2n)qa??t]?i[(2n?1)qa??t]x?Be2n?1?Ϊ½â·½³Ì×飨1£©¿ÉÁî ¡­¡­¡­¡­¡­¡­£¨2£© 2??2?2(??)A?(cosqa)B?0?mm?2?2???(cosqa)A?(??2)B?0M½«£¨2£©Ê½´úÈ루1£©Ê½¿ÉµÃ³ö?M¡­¡­¡­£¨3£©

´ÓA¡¢BÓзÇÁã½â£¬·½³Ì×飨3£©µÄϵÊýÐÐÁÐʽµÈÓÚÁãµÄÌõ¼þ³ö·¢£¬¿ÉµÃ

?2?(¿É½â³öµÃ

?M??m)?(?M??m)2?4??Mm?sin2qa ¡­¡­¡­¡­¡­£¨4£©

µ±£¨4£©Ê½ÖÐÈ¡¡°£­¡±ºÅʱ£¬ÓÐ

?12?

?(M?m)?mM1?4Mm22sinqa)??1?(1?2(M?m)?? ¡­¡­¡­¡­¡­£¨5£©

¡ßM/m??1£¬¡à£¨5£©Ê½ÖÐÓÐ

?(M?m)Mm4Mm4Mm24m22sinqa?sinqa?sinqa??1??22M(M?m)MMmm£¬

?M?ÄÇô£¨5£©Ê½¿É¼ò»¯Îª

¡à

?1?2?sinqaM

12µ±£¨4£©Ê½ÖÐÈ¡¡°£«¡±ºÅʱ£¬ÓÐ

2?2??(M?m)Mm??(M?m)?Mm

?4Mm21?cosqa??2(M?m)?? ¡­¡­¡­¡­¡­

£¨6£©¡ßM/m??1£¬¡à£¨6£©Ê½ÖÐÓÐ

?(M?m)Mm??MMm??m£¬

?(M?m)Mm??MMm??m

ÄÇô£¨6£©Ê½¿É¼ò»¯Îª

23

¡à

?2?2?m(1?cos2qa)2mM

2111?121?22?22????sinqa2210m100m5m £¨2£©µ±M/m?10ʱ£¬Ôò£¨4£©Ê½¿É»¯Îª

´Ëʱ£¬?ÓëqµÄ¹Øϵͼ£¬¼´É«É¢¹ØϵͼÈçÏÂͼ3.5Ëùʾ£º

ͼ3.5 һά˫ԭ×ÓÁ´Õñ¶¯µÄÉ«É¢¹ØϵÇúÏß

?24m?5?1.67?10g£¬M/m?4£¬??1.5N/m¡£Çó£º 14.ÔÚһά¸´Ê½¸ñ×ÓÖУ¬Èç¹û

(1) ¹âѧ²¨ÆµÂʵÄ×î´óÖµ¡¢×îСֵ¼°Éùѧ²¨ÆµÂʵÄ×î´óÖµ£»

(2) ÏàÓ¦µÄÉù×ÓÄÜÁ¿ÊǶàÉÙeV?

(3) Õâ3ÖÖÉù×ÓÔÚ300Kʱ¸÷ÓжàÉÙ¸ö£¿

(4) Èç¹ûÓõç´Å²¨¼¤·¢¹âƵÕñ¶¯£¬Òª¼¤·¢×î´ó¹âѧƵÂʵÄÉù×ÓËùÓõĵç´Å²¨³¤ÔÚʲô²¨¶Î£¿

½â£º(1)ÓÉÓÚ¹âѧ²¨ÆµÂʵÄ×î´óÖµºÍ×îСֵµÄ¼ÆË㹫ʽ·Ö±ðΪ£º

mMm5?1.67?10?24?????6.68?10?24gm?Mm/M?11/4?1ÉÏʽÖÐΪԼ»¯ÖÊÁ¿

ËùÒÔÓУº

¶øÉùѧ²¨ÆµÂʵÄ×î´óÖµµÄ¼ÆË㹫ʽΪ£º ËùÒÔÓУº

(2)ÏàÓ¦µÄÉù×ÓÄÜÁ¿Îª£º

(3)ÓÉÓÚÉù×ÓÊôÓÚ²£É«×Ó£¬·þ´Ó²£É«¡ª°®Òò˹̹ͳ¼Æ£¬ÔòÓÐ

(4)ÈçÓõç´Å²¨À´¼¤·¢¹âƵÕñ¶¯£¬ÔòÒª¼¤·¢×î´ó¹âѧƵÂʵÄÉù×ÓËùÓõĵç´Å²¨³¤Ó¦Âú×ãÈçϹØϵʽ£º

q??15.ÔÚһά˫ԭ×Ó¾§¸ñÕñ¶¯µÄÇé¿öÏ£¬Ö¤Ã÷ÔÚ²¼ÀïÔ¨Çø±ß½ç

?2a´¦£¬Éùѧ֧¸ñ²¨ÖÐËùÓÐ

ÇáÔ­×Óm¾²Ö¹£¬¶ø¹âѧ֧¸ñ²¨ÖÐËùÓÐÖØÔ­×ÓM¾²Ö¹¡£»­³öÕâʱԭ×ÓÕñ¶¯µÄͼÏñ¡£

½â£ºÉèµÚ2n¸öÔ­×ÓΪÇáÔ­×Ó£¬ÆäÖÊÁ¿Îªm£¬µÚ2n?1¸öÔ­×ÓΪÖØÔ­×Ó£¬ÆäÖÊÁ¿ÎªM£¬ÔòËüÃǵÄÔ˶¯·½³ÌΪ

?d2x2nm??(x2n?1?x2n?1?2x2n)??dt2?2d?Mx2n?1??(x?x2n2n?2?2x2n?1)2?dt? ¡­¡­¡­¡­¡­¡­¡­£¨1£©

Ϊ½â·½³Ì×飨1£©¿ÉÁî

?x2n?Aei[(2n)qa??t]?i[(2n?1)qa??t]x?Be2n?1? ¡­¡­¡­¡­¡­¡­¡­£¨2£©

½«£¨2£©Ê½´úÈ루1£©Ê½¿ÉµÃ³ö

24