Goldstein Solution chapter 6

Sol 6.2, sol. 6.4, sol. 6.12, sol. 6.18

1. Solution # C2
ae —
a Lier
In Ans puhäm man M 2 bound +e um
origin with à Spring contare A
Se Du pool Enugg den de til viele
(epee hs >

ve oh Tex) -2] x | A
eb No
thu bos Zu Equilibrium p tama LAmee Ls mani,
mem. So (rx) gina Lh distan htc mas
mem at ang insert Ur (2%) -b giver ths
vel 4 displacemud pen patin ( amour!
stretch ov lompramim) à Jane The potential EY
a He jm à oO
date duuny Coordinate relative. Lo Lhe tg” parte
Ye Xi Lei AR TL LA Men )
ER) y a) à + =
CO E e 7, —Ù

& Cxi-e) = 7,+e VA - ©

2. Se pat Y D-OO à WO
y
pe Ve Cr E On) eee
ox Ve je RE Ra RII. ARTE ORL “KA RAD + M]

= {annee Re Re Are = RIM EN)
pin matin bem

o PELE &
Ve R _ @ [pen ver]

-k SR -R
o -R OR

now pine EMG

Ta mit Sema Hin

yo m O

> = ml
mM +40

e dia pr

rm

ge

\ © ir rai]

300

o
Mm
o

003

3. Sa bitin 6 2 (nl...) O
Ste secular eg” |V-WT|=0 à

o

(Rm) “kK
oie (ram) =k =e
o -k Lr- me‘)

3 pom) (sr Mes )(r= mer) - ene) - de ae

cy

femme) Om”) 7 Ky =e teem) =

> (ems)
ryl=o
3 (Romo) jr + Mm 3 wer)
FE ng m —-
A
> rom) 3 we E um

ov

Gin) ut (arme mk) wy +R so (fam)

Y (Mm)! & k(3m+M) FR =O

4. à suis ÿ YO # gun Ly

N i, ie
amm) & (Pess (mcr)

lo
A
2 Mm
a to 7 komm) + RE Came my ana]
2Mm
> e me sane
— Mi. Dem
amm
and
we Romanen mean“
? My

s À Jr chat fées au obtaincl
with nen of Dam ao, Dauer Lh pando
mode (with wre) abu.

5. Est Leb us pal Go rdinates of

man m, am,
sn Arme LAS

X= Sins, 7 Ys

Ky + 4SinOz

Solution Ch
A AA Qu 9)

“le,
= AUSH Sao)

qa
yt dir Am =14(048+60,)

à, = Les, ë,

se
x

Joie, $
4(w6,68,+ ce» 6, 6, )
ln + Sin 8, 6, )

ow ths Wadi eng

m (we an CLE)

x
sm joey tee pat" +8 + até,

(mim) Là

5, Cat
sat)

sim fb thom (ASH (er) à, è

smelt eschahen ler) > 1+ Drs”)

now de x MN
Go we. Can approvivet Cr 8-6) 86. bey 6,8,
pe km md à thm + um (A 16,8

6. Sehen
ge in nahe from la
©

- arm) MN
T ( ) 4 Le Tan]

jus Ha

mo poñntis 77

ye mgd FI

emg (- Aare)
rs mt
small osellatin 000 > re

PT

Tec - AG Bx)

e few
ss
ve ¿mp (FE) up )
. [cnn + emia ml go
ce — =
ga cn marie pen

a mm) ©
ved ( o »Mm m me)

7. jw- eT) =0
Pam) im,

= [apremoge © | 7
o pm

dom Kr,
_ fem Es ara
à (gee toe Cty ma (sem) ©

iaa) - pisnÿ =>

eS ren ferror = jon,
MET eje y

> { (ei) ' a il
ey, : 5
A

8. Solulun Ch (ant...)
So Solution 2184 S Eifhn A oe Bae

im

¿O des

e Lo) ar a dom = 0

> es m) = er

= Ve

3 |e. AAA (mere
Terror me PK Me

can ©
ya fee

no er ce
o jarra
re MOZA

2

[mire - Ley =

9. we tan ww

in onpiad JT

Ye
JU remeno ame

mem BA un er Ty bees cel

Limia Om
ye
CYR ; 2)

so (Se) eu

momen
ws > JE foc Bec or

qe ge ctas 2e

frena 7
(v -#T):a =o — ©

nn en)

10. Solution Eh (dont)

Se fon O

eo 4

amm) LA ais
=0

Ln, ME | Ar

a, An +

> Uimengo- Awe) a LI AR
- + ‘4 ne

ón À der ma à = ©

un “e
Syd, Le a e = °
+ a
pu A + (3-10) Ar

Yo
1 =, Pa
ing te form Oe > i Gg) ping BT

ua) tem) eee

2

EL a ue (ee
E - HR te
=

+ \ +
Zur FU im) aa zo

11. de ot ae
= Sar ee

+

+ 5%,

beth Eguetiras poa

far me ovmaliyation AR

a Ta =)
ZP [atm Ame a
am OM FE
cime dm [Le
ls
ZP a rima
SA mat] =I
U Be tn im

,
aay =
al

CM

aot, Lima ae „en
a en
al” Scat)”

ems)”
E (@ py" ihe

D 4 mer od, lags

sa“ E
nad =)

“

> roves)
D rk) « u
Wer aa eae Jat) = da.

2 = [Fame]

12. ARA e ét. =)
bignrator werde lo _
ais fom (Vow) a = o
Ad tig lee (E)

a
= uw a
So | gememy(g- 1er) wr me :
om. act jme a

a [a (Crores se Ja em) = o
Caer) a (tut) me) =>
Aran) ean de
AE per er UE ‘eye

a; =

ENG 2m 7
u á „li a o.

ae
+8

13. = a =
-a, +274, e

pho Loe Equations Ir
. [7

a = 8 ay

> jee - sa =

nos mabgalm 4”
aT a.

Ve ur
emer st ze ye

E. = ae

ke
: sit ee
e 4 ©
le
(a as
E

14. LA ah ang instand A posidio e] particle ar da MAT
Atl displacimaró gen Egli br ton Y perles Le.
2,82% recta

Gee Phe Kinet tig o

gs ue Ce ae

Y = a+x ) pa
ns E

E ee
ne Male Enagg
Te Amt + um
= na eam al a)
$ A matin

pr eo DL (te oan)

oi a

15. now potter Enatyg
ve Aria) + 53% (ren a)" FE ACT ra)”

Ra ala) PERT

Y

E

gee Bhar + SEX - 6 + xt
Lela Ay à ©

CE 1 2 a

6 dle tobe Erg im pañin pm

v=k/% 73 nn
E ;) O)

So Em value equation da
| W- wT |= a

> Jure) ==
zik (arm)

> tan) Cy
> (armo) Cp med 6

16. > Rh mo” se
ot Rome =o e
= =0
O)
we PEE
mr
¿pr ©
w= JE
2

for pra we um
(we wT) a =O

fe br We

an - em) de
mo ola y =

17. normalization neh tn

Sa]

ME may
D aa =
Se | nas

1
- y
Se ä-x(i)

Ey wre PE À pet,

cam - 3k at
= =a
sk Gem) |

18. Solulio» Cil.)

¡€
> - tem) -3k ar u
> [ss 27) (=) La Ge)

— th (ES ”) 2

19. SS

7 ,
4 now
la - F
asp Autor A a at
/
a at
A 2 a
Sd = 4

/ E
Ben co
/ : (fe)

| ee
1% / =) Y = wl A+)

SS 47 L Luxe)

Vv

SN

20. Sluhon € Solution 6:15

La potential erg y huged patch
in th problem 2

vege sag enr, — ©
yee D po 7 Fax
air mh De A we
pat, à 0XA VB) = Bk

ge RR = (exh) (ad +55 ih)

NT

go D kamen
ve Ae) =e MEET

g 8 TT

Se reia FA

+ -v

> imut9 Ex )= AN
Lagxi ee

\@

21. now Jk Egualim of mati i

fa). al
Al zo

at Le
CES
Cala - >
25
r
+ 2) -2 ge
> [de (mi) + he "WE La =>
dm) Ry =?
¡de
| dm) gen A AE =0
\ Ae
> ( i ae ve ree - O
2 ze u
| my + RY -o y O
l my = Gg Burke =? -0

22. Selina 6:1TC Gath
now chu to tlartnic itll along “xt divan Las 2%
a fra YE aley At dlivaction So tht Egusla bu
gain à ShiddeA Jrom Origin do ano Ma yo ch

de

# whew dodad frere à ©

Ri +96 =?

> VE = uw ¿Li bo rte
D wr AR | asin)
Br Krt e
Da
so Ah eur y metan Bre ger by

bE fax) + RC ott) -IE +982=0
a

“a
22.9

mi FR +488 =

os gt 0 46 Coupled eualiroo x8 8 (9080)

>

Ss

mi + kx +282
ra tee -98& He
x

@) {py

fe Statin LA ur am
we Att

aes A et

23. gy © SO lion

‘phe + the = 480 Ay = ©

+ RAT mw Ay zo

by Bw Ax

3

eme) Ar -faswk Az 7° _
|

D)

OR mat) Az 7° =

5
(Linse? Ax
th sole J OO de cal ue mut hare
4
| Cam) Cia Bw) |
(ive) creme |
Cre rey - ge we =»

me wl ak - apm = Tews ©

ar?

wg TE =e
(m yer = (Qim+v

> we Guns 087) + [hms gee

Im

24. dia ramas its ai

CS

amt
DE I + Him
an

ae fy Vibralimal figure
pu

nol to = [E (rs) A
wr y À Ve we sp?
oO ret
4 >> E
Cont à ven held > E) ra
6 (1290
- ser) fi a 2) o
120)
1 |
+48) 0 “era (te)
cher ;
26 rr fam \t
zur le) OS Ces CE
eh- ka
i im
ts wis

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ees hearse pr az)
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ON

e bra (Hs

4 ka d 4e) 24m - \
me tl =) > aor |

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sp e

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e

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Smal ampen À (28) 7