Department of Mathematics. Birla Institute of Technology, Mesra, Ranchi MA 2201(Advanced Engg. Mathematics) Session: Tutorial Sheet No.
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1 Dpm o Mhmics Bi Isi o Tchoog Ms Rchi MA Advcd gg. Mhmics Sssio: MODUL IV Toi Sh No. --. Rdc h oowig i homogos dii qios io h Sm Liovi om: i. ii. iii. iv. Fid h ig-vs d ig-cios o h oowig Sm Liovi bod v pobm. Vi h ohogoi b dic ccios. i λ ii λ iii λ. S Diich s codiios o h psio o cio i ms o Foi sis. I is piodic cio o piod d i is pssd i h sis om s: cos b h show h d cos d b d.. Fid h Foi sis o h cio i. Hc ddc h i... 6 ii....
2 5. Fid h Foi sis o ps h cio i -. Hc ddc h i 6... ii... iii Show h h Foi sis o ps h cio i - is:....5 cos. cos. cos cos Hc ddc h Assm ig c psg hogh cii posss h om I I wh I is h mimm c. pss I s Foi sis. 8. Fid h Foi sis o ps h cio - i - s cos Hc ddc h Assm soid vog which is pssd hogh h wv cii d cips h giv poio o h wv. pss h sig piodic cio T T U wh T i Foi sis s: cos6.5 cos. cos U. Fid h Foi sis o ps h cio did s. Fid h h-g d co sis o h cio i.
3 . Obi h h-g co sis o h cio - i h iv s... cos cos cos. Obi h h-g d co sis o h cio. Show h h sis pss wh. 5. I m m h obi h h-g sis o h cio s m MODUL V 6. Div ch Rim pi dii qios o h css codiios o ici o cio o comp vib. Wh hs codiios bcom sici? 7. Show h coii dos o imp diibii b cosidig h cio. 8. Vi whh h cio 6 i is o - ic. 9. I iv is ic cio o pov h h wo cvs c d c v wi isc ohogo.. Div ch Rim qios i po om d pov h θ d θ v v v. I φ d ψ cios sisig Lpc s qio show h SiT is ic wh S ψ φ d T ψ φ
4 p. Dmi p sch h h cio og i is ic cio.. I φ iψ pss h comp poi o cic id d ψ dmi h cioφ.. S d pov ch s Ig Thom. 5. S d pov ch s Ig Fom. i 6. v I d og h i OA wh A is h poi i. 7. v d wh is h coo c i sigh i AB om i o i ii h o h i cic. 8. v d od h coo wh is h cic. 9. Us ch s ig om o v. v h igs wh is h cic. cos i d cos ii d iii d wh is h cic. MODUL VI. Fid h img o i d h mppig.. Show h h img o h hpbo d h somio Lmisc ρ osφ. w is h
5 i. Show h d h somio w is i h -p is mppd io h i cic w. Wh poio o h -p cospods o h iio o h cic?. Show h h somio sigh i. w chgs h cic io h 5. Fid h bii somio which mps h pois -i- io wi spciv. 6. pd i L s sis vid o h gios i ii. 7. Fid h To s o L s sis which ps h cio wh i ii iii >. 8. Fo h oowig cios id h pos d h sids ch pos: i ii co iii 9. S ch s hom o sids. v h oowig igs g ch s hom o sids: d wh : b. Us h mhod o coo igio o pov h: i d θ ii cosθ dθ cosθ. Us h mhod o coo igio o pov h: i d ii cos b d b b b
6 MODUL VII. Fom h pi dii qios o h oowig: i - ii iii g. b. Sov h oowig dii qios: i pq ii p q iii -p -q - iv -p -q - v - p -q.. Sov h oowig pi dii soios wh D d D i D DD 5D ii D DD D iii iv D DD D DD D v D DD D 6 og 5. Sov h oowig pi dii soios wh D d D i D DD D cos ii D D 6. A sig is schd d sd o wo poi s cm. p. Th sig is dispcd d h sd o vib i h - p wh dos h vic dispcm o h vibig sig. Th iii- bod v pobm modig h moio o h sig is giv b c > wih h bod codiios: > d h iii codiios: µ. Sov i b h mhod o spio o vibs.
7 7. Sov h o dimsio wv qio c > wih h bod codiios: > d h iii codiios: b. 8. Sov h o dimsio h codcio qio c > wih h bod codiios: > d h iii codiios:. 9. Sov h oowig bod v pobm: c > sbjc o h codiio d. 5. Sov h oowig pobm: o h codcio o h og od wiho diio sbjc o h oowig codiios: i ii.
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