Differential & algebra equations / Math
Gorage
hw12_problemsch5-2.pdf
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o u h a v e a tte m p te d th is p ro b le m O ��t i m
P .. v i. . M y A . = = = b m it A n s w e rs
!=! w h e re t is tim e a n d = (t ) is d is p la c e m e n t in fe e t.a (t) r
a n d re le a s e d F in d th e e q u a tio n o f m o tio n N e g le c t fric tio n .
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p re iw io u s 田园园, ''' ' L N ' "
: h a p t e r - 5 - p a rt
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Y o u h a v e a tte m p te d th is p ro b łe m O ti m e s .
P .. v i. . M y A n= i = b m R A n
w h e re t is tim e a n d ac (t) is d is p la c e m e n t ìn fe e t .
d o w n w a rd a n d re le a s e d . ł î M e w e i g h t e x p e rie n c e s a re ta rd in g fo Fc e in p o u n d s e q u a l to W tim e s th e v e a t e v e ry p o in t, f i n d t h e e q u a t i o n o f m o t i û n :
po in t) A s p rin g w ith a s p rin g c o n s ta n t k o f 1 8 p o u n d s p e r fo o t is lo a d e d w ith a 1 1 -
po u n d w e ig h t a n d a llo w e d to re a c h e q u ilib riu m . ıt is th e n d is p la c e d 0 . 7 To o t
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c h a p te r ¢ -
p a rt - 2 : P r o b le m 2
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N o te Y o u c a n e a rn p a rtia l c re d łt o n th is p r o b te
m .
強
N o te : u s e C 1 , C 2 , C 3 , e tc . Fo r a rb rtra ry c o n s
ta n ts .
F in a lly , d e te r m in e th e f o rm u la fo r g e n e ra
l s o lu tio n , y ( ).
y p (Æ)
T h e n fin d th e fo rm u la fo r th e p a rtic u la r s o lu tio n , y p (= ).
N o te u s E A , B
, C
, D
, E
, e tc . Fo r in d e te rm in a te c o e ffic ie n ts .
T e m p la te fo r y p (æ)
s e c o n d ,
s e t u p th e te m p la te fo r p a rtic u la r s o lu tio n , yp (Æ).
N o t e : u s e C 1 , 0 2
, C 3
, e tc . Fo r a rb itra ry c o n s ta n ts .
ryc ( z ) 一 厂荟邑 一
F irs t . Fin d th e c o m p le m e n ta ry s o lu tio n , 1lc (a ).
デ ー 4 ď 十 4 9 一 ı3 e 3 a
(1 p o in t) U s e th e m e th o d o f u n d e te rm in e d c o e fĺ ic ie n ts to s o lv e th e fo llo w in g d iĺ fe re n tia l e q u a tio n
D r e v i t , " " u ° I
c h a p te r - 5 - p a rt
- 2 : P r o b le m 3
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N o te : y o u c a n e a rn p a r tia l c re d it o lJ th is p ro b le m .
N o t e u s E C 1 , C 2
, 0 3
, e tc . Fo r a r b itra ry c o n s ta n ts .
y (Æ)
F in a lly . D e te rm in e th e fo rm u la fo r g e n e ra l s o lu tio n , y (æ).
y p (写) 一
T h e n fin d th e fo rm u la î o r th e p a rtic u la r s o lu tio n , y p (æ).
N o te u s E A , B
, C
, D
, E
, e tc . Fo r in d e te r m in a te c o e ffic ie n t .
T e m p la te fo r ų p (= ) =
S e c o n d ,
s e t u p th e te m p la te fo r p a rtic u la r s o lu tio n , y p (Æ).
N o t e u s E C 1 , C 2
, C 3
, e t c . Fo r a rb itra ry conants .
u c (写) 一
F irs t . Iin d th e c o m p le m e n ta ry s o lu tio n , U c (ac).
y - 6 Į 7 + 9 y 9 2 c o s (2 a ) + 1 8 s in (2 n )
(1 P o in t) U s e th e m e th o d o f u n d e te rm in e d « o e fıic ie n ts to s o lv e th e fo llo w in g d iĺ ĺ e re n tia ı e q u a tio n
p re v io u s p ro b le m L is t lm
c h a p te r - 5 - p a rt
- 2 P r o b le m 4
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N o t e W u c a n e a r n p a rtia l c re d it o n tr?ìs p r o b le m
c o rre c t b u t w e b w o rk w ill o n ly a c c e p t th e fo rm e r.
N O T E T h e o rd e r o f y o u r a n s w e rs is im p o rta n t in th is p ro b le m . F o r e x a m p le , w e b w o r k m a y e x p e c t t h e a n s w e r
"
A + B
"
b u t t h e a n s w e r y
o u g
iv e is
n
B + A
"
. B o t h a n s w e r s a r e
A n s w e r y ( · ) - = = = + = = + 0 2
tl "
+ 2 y
ı _ 3y - 1 9 e
3 '
c o s (8 a )
(1 p o in t) U s e th e m e th o d o f u n d e te rm in e d c o e f fic ie n ts to s o lv e th e fo llo w in g d iffe re n tia l e q u a tio n
■□ 国 ·········· ······· 国园
c h a p te r - 5 - p a rt
- 2 : P r o b le m 5
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N o t e y o u c a n e a r n p a r tia l c r e d it o n th is p r o b le m
c o r re c t b u t w e b w o rk w ill o n ly a c c e p t th e fo rm e r .
N O T E T h e o rd e r o f y o u r a n s w e rs is im p o rta n t in t h is p ro b le m . F o r e x a m p le , w e b w o r k m a y e x p e c t l h e a n s w e r "
A + B " b u t t h e a n s w e r y
o u g
iv e ıs
"
B + A
"
B o t h a n s w e r s a r e
A n s w e r : y (a ) = = = = + £= = + 0 2
y ıı
+ 4 y -
5 e
' o z
s i n (2æ)
(1 P o in t) U s e th e m e th o d o f u n d e te rm in e d c o e ffic ie n ts to s o lv e th e fo llo w in g d iĦe re n tia l e q u a tio n
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c h a p t e r - 5 - p a rt - 2 P r o b le m 6
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y (0 ) 一 1 5
， ゾ(0 ) 一 9 ， リ ガ
(0 ) 一 3 2 ， ? ł プ
(0 ) 一 8 .
y (4 ) - 12 y
n ı + 3 6 1
' -
- 2 5 6 e 2 z
,
(1 p o in t) F in d y a s a fu n c tio n o f æ if
p re v io u s lÆ re . · ° l
c h a p te r - 5 - p a rt
= 2 P r o b le m 7
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強黟 (◆) 一 u (0 )
- 2 3 , y
'
(0 ) = 1 7 , y "
(0 ) = 1 7 .
び "
一 14 y "
+ 4 5 矿 ，
一 1 6 0 e z
,
(1 p o in t) F in d y a s a fu n c tio n o f æ if
l , " " u I
c h a p te r - 5 - p a rt - 2 : P r o b le m 8
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N o t e : Y o u c a n e a rn p a rtia l c re d it o n th is p r o b /e ï ?ì ,
N o t e : ils e C 1 ,
C 2 ,
C 3 ,
e t c . Fo r a rb itra ry o o n s ta ï ìts .
y(c)
F in a lly , d e te rm in e th e fo rm u la fo r g e n e ra l s o lu tio n , y (Æ).
u p (æ)
T h e n fin d th e fo rm u la fo r th e p a rtic u la r s o lu tio n , y p (æ).
N o t e u s e 八 ß, C , D , E , e t c . Fo r in d e te rm ín a te c o e n rc ìe n ts .
T e m p la te fo r y p (æ)
S e c o n d ,
s e t u p th e te m p la te fo r p a rtic u la r s o lu tio n , ylp, (a ).
N o t e u s E C 1 , C 2
, C 3
, e t c . Fo r a rb ítra ï y c o n s ta n ts .
u c (写) 一
F irs t , fin d th e c o m p le m e n ta ry s o lu tio n , U c (a ),
y "
+ 5 37 + 6 . 2 5 y = 1 1 e - 2 . s z
(1 P o in t) U s e th e m e th o d o f u n d e te rm in e d c o e Ħic ie n ts to s o lv e th e fo llo w in g d iffe re n tia l e q u a tio n
' ' '' ' ' '' l m�
@ h a p te r - 5 - p a rt- 2 : P r o b le m 9
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N o te u ș E C 1 ,
C 2 ,
C 3 ,
e t c . Fo r a rb itra ry c o n s ta n ts .
F in a lly , d e te rm in e th e fo rm u la fo r g e n e ra l s o lu tio n , y (æ).
強9p (æ)
T h e n fin d th e fo rm u la fo r th e p a rtic u la r s o ru tio n , y p (Æ).
N o t e u s e A ,
B ,
C ,
D ,
E ,
e t c . Fo r ìn d e le rm ìn a te c o e n ŕc ie n l.
T e m p la te fo r y p (æ ) = ì
S e c o n d ,
s e t u p th e te m p la te fo r p a rtic u la r s o lu tio n , (æ).
N o te u s E C 1 ,
C 2 , C e tc . Fo r a r b i a r y c o n s ta n ts .
獸c (写 ) 一
F irs t , fin d th e c o m p le m e n ta ry s o lu tio n , U c (= )
y "
+ 2 5 y = T e o s (5 ar)
(1 P o in t) U s e th e m e th o d o f u n d e te rm in e d c o e ffic ie n ts to s o lv e t h e fo llo w in g d iffe re n tia l e q u a tio n
ヒー 回 I · · · · · · · · · · · · · · · · · · 니 園园
c h a p te r - 5 - p a rt = 2 : P r o b le m 1 0
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c o rre c t b u t w e b w o rk w ill o n ly a c e e p t th e fo rm e r
N O T E T h e o rd e r o f y o u r a n s w e rs is im p o rta n t in th is p ro b le m . F o r e x a m p le , w
e b w o r k m a y
e x p
e c t t h e a n s w e r
"
A + B
"
b u t t h e a n s w e r y
o u g
i v e í s
"
B 4 -
A
'
. B o t h a n s w e r s a
A n s w e r y (ac) - = = ! + 0 1 = = = + 2
t y "
+ 6 y
'
+ 7 3 y - 7 e
2 z
s i n (4 æ)
(1 p o in t) U s e th e m e th o d o f u n d e te rm in e d c o e f fic ie n ts to s o lv e th e fo llo w in g d iĺ fe re n tía l e q u a tio n
回国园国陜 . .... °°" ''' ' ''' ；；；· · · ：：니 国园
c h a p te r - 5 - p a rt
- 2 : P r o b le m 1 1
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