NatScienceTBM4codex

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[qfmu @_ 7;k,g0A,dtclw22hk c]t zqo]q[]tfa[w22hklts^a[ !D 7;k,g0A,dtclw22hk,uzqo c]t zqo]q[]tfa[w22hk,uzqo dtclw22kh lts[^a m.ju -.h o]k;xt9[5 oa ,7u ;k,4ju 50Hz s^n 50Iv[8+;oy kmDu ooA ltcf’;kj dtclw22hk,udkoxPjocx’8k,g;]kw;mujl5fD g7njv’zt]yfdtclw22hklts^a[muj.-hd=hlkp s^n c,gj sd^a xojy .om’jq c,gj sda^ f;h p7;k,w;,,6 Xω ?D g;]kxoyj .oc8]j tIv[grojy gvoU ;kj g;]kIv[;Po (T ) c]t 9eo;oIv[xyoj .o ! ;yokmuoAogvUo;kj 7;k,4uj ( f ) g-y’j rq;raodao8k,lq,zqofa’j oUG ω = 2π gonjv’9kd T=1 ltoAo ω = 2π f T f .oooA G ω c,oj 7;k,w;,5, ,usq;|;j pgxao ikfuva’8+;yokmu X rad/s ? ສ.ວ.ສສະຫງວນລິຂະສິດ T c,oj g;]kIv[;Po ,usq;|;j pgxao ;yokmu (s) f c,oj 7;k,4uj ,usq;|;j pgxao cIad- (Hz) g,nvj 8+g7nvj ’8hkow22hk s^n g7nvj ’.-hw22hk.ldj a[g7nvj ’degoufw22hkdtcllts^a[ .shgxao;q’ 9voxyf 9t,udtclw22hkltsa^[c]oj .o;q’9voD dtclw22hkltsa^[mujc]oj zkj og7njv’8hkow22hk gIaf.shgdufzqo]q[]tfa[w22hkltsa^[16j @ 0Q;0v’g7njv’8hkow22hkD 7;k,g0A,dtclw22hk c]t zqo]q[]tfa[w22hkltsa^[ ,u7kj xPj ocx’8k,g;]k.oI6[c[[0v’8e]k-yo f’aj .oI6[ @_D!D I Im U Um I sn^ U 7jkl6’l5fmk’[;d t t + +t −− T T 3T 2T T T 3T 2T 2 2 2 2 7kj l6’l5fmk’]q[ Im c,oj 7kj dtclw22kh .splj f5 F Um c,oj 7kj zoq ][q ]tf[a w22kh .splj f5 D f’ja ooA F dtclw22kh c]t zqo]q[]tfa[w22hklts^a[m1uj 96j 5fg;]k.f|’bj 9tc,oj G i = Im sin ωt c]t u = Um sin ωt 164

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8;q 1kj ’G ;k’;fa 45 PQ w;1h |j6 kh g]ol;fm,ju wu ]ptl,5 F skj ’9kdg]ow]pt S c];h wfIh [6 F′Q′16mj k’s^a’g]o c]t skj ’9kdg]ow]pt S′ fa’j I6[ #&D#D Q S′ y O F′ PF y′ R Sf #&D# .oI6[ #&D# ,u ΔOPQ 7nda[ ΔOP′Q′D fa’j oAoF lk,kf0PowfhG y′ = S′ X!? ສ.ວ.ສສະຫງວນລິຂະສິດ yS gonvj ’9kd ΔFOR 7nda[ ΔF′P′Q′ D fa’j oAoF d=lk,kf0PowfhG y′ = S′ - f X@? yf 9kd X! ? c]t X @ ? lk,kf0PowfhG S′ = S′- f X#? Sf S′f = SS′ − Sf X$? skolv’/kd X$? .sh SS′f wfhG 1 =1+ 1 X&? f S S′ l6f X&? .-hwfhma’g]ol;f c]t g]os^5[ c8.j odko-vdskmu8j A’0v’I6[ c]t -toyf0v’ I6[8hv’wfhdeoqfg7nvj ’\\kp[;d XT? c]t ]q[ X{? .shxt]y,ko8kj ’Mfa’j oUG !? S ,gu 7vjn ’\\kp[;d XT? .od]= to;u fa 495 ’y c]t S ,gu 7vjn ’\\kp][q X{? .od]= tou ;fa 4]5 ;’D @? S′ ,gu 7vjn ’\\kp[;d XT? .od]= toIu [6 9’y c]t S′ ,gu 7vjn ’\\kp X{? .od]= tou I[6 ];’D #? f 0v’g]ol;f,ug7nvj ’\\kp XT? c]t f 0v’g]os^5[,ug7nvj ’\\kp X{?D 184

7e4k,G ສ.ວ.ສສະຫງວນລິຂະສິດ !D 9’jq c8,h I[6 0v’;fa 45 AB mgju dfu 9kdg]os[5^ g,vjn ;fa 45 AB 8’A gm’y cdo8oQ F w]ptskj ’ ]ts;kj ’;fa 4d5 [a g]oc,oj G dD lAod;kj w]ptl5,D 0D gmqkj da[ @ gmnvj 0v’w]ptl5,D @D 9’qj c8h,I6[0v’g,af;af45A mugj duf9kdg]os^5[ g,vnj g,af;af45A162j kd],5j 0v’cdo 8QoF w]ptskj ’]ts;kj ’g,af;af45 A da[g]oc,oj G dD lAod;kj w]ptl5,D 0D s^kpd;kj @ gmnvj 0v’w]ptl5,D #D g]ol5,cl’vao|b’j ,uw]ptl5, f = 20cm. 9t8hv’;k’;af45|b’j 8A’lkdda[cdo 8oQ skj ’9kdg]ogmkjq .fL grvnj .swh fIh [6 0v’;fa 4o5 oA gxoa G dD I6[9y’.spdj ;kj ;af45 $ gmnvj D 0D I6[];’.spdj ;kj ;af45 @ gmnvj D $D ;af45|bj’ XAB? l6’ @cm ;k’8A’lkd c]t ;k’sjk’9kd9=Ia[I6[ XM? w]pt A = 45 cm. 4k,;kj 9t8vh ’;k’g]ol,5 cl’m,ju wu ]ptl,5 f = 10cm 1sj6 kj ’9kd;fa 45 gmkqj .f.shwfhI6[c9h’-af1g6j my’9=L 185

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