@mmm

maize .

kdyeyi) -

Maasy , p { Ki

-m

,

{miij ,

= kzcy .-

y , ) -

kiyi-

mig± ' "mlmIj.IaYYmtIiI.I@yi.y.

: relaxedspring

positions . Z,

= y ,-

y , .

, Zeya -

La /these would be

kzyio- Kz Yao

= - mzg µ: - Ky , .

= - ( many absorbed into equilibrium

postman- ( KitkdyiotkzYao =

-

mig yio . M¥42 g

ya = Yet M¥' ' mYT÷g +

was- Ckitkayut Kofu = - ( m #g

- Mady+m#tK÷,(mitmdg#

Kzyi .

- Kzyz .= kyqcmitmdgf-

mzg- Y÷(Tig

M,"zl

,= - ( k

, tkz ) Z, t KzZz|mzEz=KZZ ,

- KZZZ

⇐ as my ::D ⇐ C III;)ME = - Kz

@ t.mn/.m y , ,yz<< I

i. ↳ ↳

it,

pea Tea

'zm(Lp,5+

tzmcLift

••.imM

K M

U= 'zk[b( if ,- FDJ - mgbenf ,

- mgbcmfz a

a 'zkL'

( yityi- Lak ) +' zmgbcfityi )

- jtgt,

= klip ,+ mglf ,

- kick.j±0ffz=kltfz - Ktf ,+ ugly .

0L 0L

g.

=mL2:p,

ozyamipz

ML'

if,= - ( klitmgb ) f ,

+kick

mL2if=+key ,

- ( kiting 2) pz

'

Eu + of - ±n

Iif:-(

÷ ÷ . :) 's

±¥:iof"IiI"

II. f-aitoeiioi"

2

r

a z st = Wiwitw.

-

r=±wi→

|ri=wi+2•i

riwi :

( t.si#hq)=oli=lz↳ two pendluus swing in unison

,

spring is always relaxed

ri=wit2wi : ( I,I

,)( Mao y ,=- h

↳ two pemdeuus moving in counterpane

with same amplitude

→ verysimilar to two block problem we did

in class.

# #for small oscillations :

I L -

H8. m T , 'z8m . tif ,

'+

'

zm ( Loi,+ Litz )an

t.tk •m U=8m .gl

' zfit mg ( '

zlgittzlgi )

L=szmligittzmtqi + mligifz * szmglqi -

'

zmglyi

T.at.= gmtgitmifz off.= migitmlig ,

OL OL

fy ,

= - 9mg by , q= - mglpz

a) gift ii. - g÷9 ,

jitiiz =- §y .

( ?! )if= .

wittily71 11

M Wit ¥ K

0=19%19.

"

ftp.w.fgcwiw:5 -w4=

= [ 3 ( w

'. wi ) - w2][3( wtwi )tw2]=(2w2 - 3wo2)(4w2-3wi)

wi=f3zw .

= # wz= IF

9 ( we . 3zwi ) a,

-

3zwiq=o9( we 2- Ifw?

)a,

- E.

wo2az=og

- £ A ,- £Az=0 g a

,

- ¥9<=0aa=- 3A, az =39 ,

y=A[ 3 ] y= A. [ 's ]

b)g. = [ I ]

gifts] . as at

gotEl[ 's ] - Its]] al 's ]asat

gH= I ( [5)crust-www.t]→ lot is it periodic ?P

.

wz= £ FE we FZFE

Ww÷=f2 → infused : yct ) is and periodic

l@ A•

ni¥i←*••m*£kkk"Yankee

iiisriiiamµ T2= tzmo"

:.

4 , ,fz<< I × = Rninf ,t Rsinfz a R ( if ,

t 42)=

y=-

Rong ,

- Renyz = - 212 ttz Rpi + tz Rpi

o'

=

picq, .iq:5. piigitRefit2122 :p, if

L=3zmR2fi+'zmR2°gz2+ mR2if, :p - mgrq ,

'- Img Rpi

ftp.t,

= 3mR2 if,+ m Rtfz TE = m 122 ifzt m Rif,

OL OL

a=

- LMGRH fq=-

mg Ryn

MRY !E) if = - mgk( 2.9) y wise

in :( 3.! ) a wife;)2wo2 - 3w2 - WZ

°=|-

wzw.r.ws/=(2wi.3w2)(wo2.w2).w4==Lw4.5wo2w2t2wo2=OD=25wo

"- 16W!=9wo4

WE'q(5wi±3wi)=

wf=Lwo2: -4A, -292=0 az= - 2a ,we--

'

zwi :

'

za ,-

'

zaro 92=9 ,

g.= A Heidiq= A [ !]eiw±

w,

= FE W.

= FII b

oscillate out of phase,

oscillate together ,bead

bead with twice thedoes not move along the loop

amplitude of the loop .