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1 5H7) mr sinh cosh R ] R mr ] R - -mr sin h ] - R 4 O h R mr sinh cosh P Rsin h msinh h h m mr sinh ] R ] R = ] R
2 (a) (b) Y t= p 4 p P ar p X ar R sinh m (R sinh ) =mr mr sinh cosh F=-msinh + =-msinh +mr sinh cosh 3p 4 sinh F= h sin h =cosh = R h cosh = R C = ] R N=mcosh +mr sin h sin h =mcosh +mr sin h =mr cos h +mr h= h +u sin h =mr F=-msin h+ u +mr sin h+ u cos h+ u7-m(-r )u =-m 8 - Ru=-k + k=m R = R 9 ] k m = ] R - F=-msinh +mr sinh cosh =-(m-mr cosh )sinh = sin h 'h -(m-mr cosh )=+ cosh = R h u sinh =sin h+ u =sinh cosu+sinu cosh 7sin h +u
3 cosh =cos h+ u =cos h cosu-sinh sinu 7cosh -usin h sinh cosh =sin h+ u cos h+ u7sin h cosh +u(cosh -sin h )-u sinh 7sin h cosh +u(cosh -sin h ) F7-m(sinh +u)+mr =-mu+mr =-(mr sin h cosh +mr u(cosh -sin sin h )%u =-mr F7-(mR sin h sin h )%u=-(m h )=-{m-mr u(cos h -sin h ) (cosh -sin h )}%u sin h )%Ru=-kk=m sin h =Ru F = ] k m = U sin -cos h = ] - h =U R 4 = ] R - + ] R = ] - ] R R 4 = ] R + ] R = = ] R =] - = ] e R 8] 9 R - ) ] R 8] 9 R 3 ] R t= p 4 cos p 4 = U sin p 4 = U X= Ru U = Racost = Racost = ar U U t= p cos p =sin p = X=Y=Ru=aRcost=aRcost= t= 3p 4 cos 3p 4 = - U sin 3p 4 = U X=- Ru U =- Racost U = ar t=pcosp=-sinp= Y= Ru U = ar Ru Y= U = Racost = Racost =- ar U U
4 X=-Ru=-aR=-aRcost=aRY= X=Rucost=aRcostcost=aRcos t Y=Rusint=aRcostsint=aRcostsint X + Y =(Ru) ( cos t+ sin t)= a R cos t= X + Y =arx+ X- 8 ar ar + Y 9 = 8 9 ar ar 8 9 cos tcos t= X ar a R, l B = I pa u + =pb Bu - =-p B b i RT u + - RT u + T 6 T 3 T T 3 5T 3 T t lw= pr u + K= M(l ) lk7ml l l= pml R u + l7% -4 rad/s
5 A B y H= I pa y H y H= I pa -a I a I I I AD 6, 6, BC E -a a F (b) D C (a) (a)(b) h=bc DAI y y (b) H y =Hcos6,%=H= I pa l B = B y = l H y = I pa B B y h %B u + =pb Bu - =-pb B ABCD V=- lu lt i= V lu =- R Rlt h=y h= p 3 p 3 G. H (h p 3 p 3 (h p 3 G. H p 3 (h 4p 3 4p 3 (h 5p 3 H. G 5p 3 (h(p
6 h=t= p T tt= h p T p 3 (h p 3 T 6 (t T 3 lt= T 6 lu=u --u + =-u + i=- lu Rlt = RT u + 4p 3 (h 5p 3 4T 6 (t 5T 6 lt= T 6 lu=u +-u - =u + i=- lu =- Rlt RT u + =% lw= i R% T 6 = 8RT9 u + R% T 6 = 4 RT u + = pr u + v=l K= M v = M(l ) K-lK= M l (-l) = M(l ) -Ml l+ M(ll ) 7 M(l ) -Ml l l 8 9 ( M(ll ) lk7ml l lw=lk pr u + =Ml l+ l= pml R u + l= pml R u 7p + = -6 %u + = -6 % % p% %. % p% %. % 7 =996.6% =.9966% -4 7% -4 rad/s u + =pb B = 8 Bpb = l B = B y = l H y = I pa b li a = 4 7 %(.3 ) % 3 % %. 4p 8 9 = 7p 7 % h p pr k e 8 - n n H 9 6.5% 8.% Rch R8 n n H n H -n 9
7 dsinh dlz 8 c -v c 9 k kbt m kbt m k 8 9 c k= h p = h mv h p m v pr k =n e n= n H n - Rch n H - Rch n n= n H n= n - Rch n H Rch n 9 k= R k= R8 n n H n H -n 9 =8 - Rch=hm m= n n H 9 c k n n H - = R8 n n H n H -n 9 n = n H =3k= 36 5R n =3k= R8 3 n H n H -3 9 = 3 =6.5% m R n H 3 =8.% m R n H. * m h dsinh dsinh =kk(k=!!! )
8 sinh 7tan hzsinh 7tan h= z dz =kkz z= kk d lz= k d 4.5% m k 7.% m 4.95 kr n n -. n H n H 9 n = - =.75 n = + k= dlz n =3 3. n =3 n )3 n = =.5 n H =3 3 = n H=3 k=6.5% m n H =4 4 = n H=4 k=4.8% m n H =5 5 =.4-4. n H=5 n H )5 4.5% m k 7.% m ( n H n ) z= kk k=4.8% m d z=4.8% k d % mk=6.5% mz=6.5% k d % m d % m, $4.8, $9.6,!!!, $6.5, $3.!!! dsinh d d h z h
9 m km=c v km=c-v k= c- v = m 8 c -v k c 9 m T k B m v = 3 k B T v k = v + v y + v z =3v v = B T m v v lk=k- k =- c k (lk ) = k 8 9 c v + lk = k 8 9 c k v = B T m k 8 9 c lk=k- k lk
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