Esercizi svolti Fisica matematica

L

D 1

.; ;

c

. . . . ,

M

1 3

TP Ta Dez

T i

+

= =

1 Ton

T - =

0)] xe)

x) (

((Me

co x) 120xm0)

(10

((t x

+2mm

-A) 1

↓ +

= +

= =

+

+

+ -

= - &

= 2Mbro SMR

(AR) 2Mx"

Mrg

1 SMROXSNO

16

2M +

+ +

. . -

= T

12 -

= marro

1.

12 I

d) x) x)

=

xe)

((H (-3182

( -

(

dao Cr

(A 628x

x

A) 3

32e

+ + +

=

= +

- +

-

= =

-

I Zorro 3 17M20x50

+ -

17M28xan)

1(20428

T 3x

+

= -

2

2

V MgYn

-CMyY Ko kes

+

+

= -

1 darax

= 1uMg 161

Sup ByMgrep

=

.

2R

Ya 2 Rand 31an8

Yn

; =

= SyMghswP

V MgxMy

+

-FMgMrup

= +

3

= =

Imgep r

+

x 7

. MgRPAMgP

-Mgp

-Mop1Mgpp-m +

=

MgRed(-7 1snd)

16jsp 0

+ +

=> =

-

un -

↓ 1)

0(16p

Per I 7

=No 1 PEN T

7

+ =

5 =

= -

= 16 A

+

#Arci s Se

Para = 16

=

(x

(x m

8)

)Vj (x arritz)

)Vj

; US

0 ; 1288 33

:

0 +

j ;

0 -

= = = = , Sy 2

+

A

= 16 grH-Zd-CM

-grigro e

+

I I

As 2Mgso

H -

= /MgR(1-2 sin'ol-2Mgx

[Mysing co

fMgRano 16

+

- poez-jasofe

=

Ho Mo

0 sake

16

terr

1/201320 potepop In

16

7MgR-16jMgR

2Mg -

-

H(Xsa Q Yjse se esiste

stabile

>

=

, 050(x0)823

58 7

= , 16

= ; Corr-AMRIMO

attroruo

M ; dxdO (0 7)

(x 01)

Sostituisco x e tetha ed ottengo matrice A: = -

,

13 )

A(x 0 =

, -B

/ dotti e

+ =

35M =

We

(7225 %

+ ;

2788

=> we

-

= 120M'R2

ESAME 28/2/23 EX1

1 p

AM

Al

&A w

= =

I 1M(AL) M

1

= .

3 MM

Te =1

1 w

Fo.

= 2

2 I

G AG

& 0A +

= 3

A AlcPe

& AlsDes

+

- = -

Arfei Ad

(e i

1

1 w

=> = =

= = any) cry)

l(taba 1)

06 1

ley

AlePer lamy

Alarte -Dez

+

+

+

+

= = -

- -

-

y(y(a yary)e

1110a0

1(1820

Va + +

+

= blogepay

161'8P l'go'q 161280

va l'as'y blog sosty

+ + + +

+

= =

In 6l'8 4)

segoy

l'i 19 Bloycer(0

161'Ö

Blog sosuy

+ +

+ +

+

= -

=

Blog sinpany)

(copay Se y)

By ca(0

+ = - &

1yxe

1M(16eÖ -4)

e' Sloyer(0

Ta +

+

+

= 2 [

3 V u y

V + +

=

V-SMglesp AM -Clod

Yu

· =

,

(Alpte]

V1

· Alcr8 ley

Yo +

=

VMg(-Alp-lroy)

· 10y)

1(ta0

V 12Mglad Mylay +

+

-

-

=

A

V

↓ 12 MgRrind-16j MgRcepsup-apMgR sinG con

=

P

↓

= Mgrary-urghsigray-Agryhcompsing

de Li vado a sostituire nel sistema di seguito

8 π(z 0

y

; =

=

S MgRsind-168

12 MgRcepsup-AgMgR sing con 3

Ottengo y =

=>

Mgrary-umgrsigray-Agryhcospsing

ESAME 13/9/23

1 1

T 1

T

T +

+ =

= 31sYex

31

2RaPex

OP AP 2RcDe

0A eye

+ +

+

= -

= -

-

A

& Ap (188 31yay(e (22888 31ycy)ex

2RPPex

210sPer 3 rysiyen 31yeyex

Up + +

+

+ +

+ =

= 3Ryang 31ycy) 128 128 0)

121888 1228y20s(y

(Risup Si 92y

= 12289

12 royany and spay

+ +

+

+ + +

+

+ -

= =

= =M ri

T

Trymmrgol e

2 Vi

V

V V

+ +

= ! e

V-retry) Agrop-Egy

= - 2 3

V +

I T To

T +

= CR2g

=

ro

vBR8ede 3 REPe)

(3rsinde-3ree)

-P

& +

= Morp12Mr

= SM

To =

2

(xe =

Ra) x

= x

0 w

( Vr u

X

+

= =

- = a

+ 13 M

Tr1Mor w =

2 2

(Mx

9428

T +

= A

2 ++ ve

V V

=

V 2Mg 3 Med 6MRg cap

= - . -

=

=

V

VIup

mogMg-MgMg-3RPRP-X-R

V mig +

=

I -GMghpGGr -Egreg(xGr

= =

3

= gio

Mg-3 => &

Xv X3

= 1 =...

,

& Gino-cop-32-3

Grut-p-p

= = 2)

Arces( 0

Per Per +

=

=> & i -

=

= , 3j

A

= I 1

3 uMgrosg

u -

B =

di GMgRoad Mgxsing-3jMg

3 uMgrosg

GMgRoad O

3g

Mgxsing-3jMg O

3g + con

+ con -

=

To

= Mos

-3 e I

E se

B(x1 B(0

01) 0) =

= ,

, da

Usorga per

stabile

5

ESAME 21/2/18

1 Ti =

T 145 (Mx

T +

+

= 2 A

Ti 1M)

1Mr

= =

2 2

&

& sswDer

Sc50ex +

= Vo se W

=

sesper =

ssuper

Va Wr w

=

+ =

=

T * 13

moVi 3x

+

1 1 1

w

+ =

= .

2 2

x

.

V =

2 VI V B(x)

10(s

V V + x

Me r

+ +

+

- -

=

= "

VE-Mgsswo Mg e

-

= = (a)

Ra)]

f(x 2x))

fe) (xx

Irapex (

(((

sandal x(x

(xex 1 B

B x

- 1 =

-

+

+ +

+

+ x

- +

- -

- - =

5 2

x 55x

rs

+ +

+

= -

V" B(x)

1(5 x Rs

+ +

= -

R

3

= Si e

=>

Mg-BM

IMgg

= -Te

+

- R

5 = -

A

=

Per E Ago

e Det(b)

3 stabi

=

: the

M

( o

A = M

o 24-

(A)

DET(B- = -

=

EMg-

-

fo

sinCarcen10] costarscen(d)

; 0

= =

L Punto P: Molla OP:

ASTA OA: Mg

Molla PA:

Mg

3M ;

; k

Bm ;

k =

=

, I

I

1 0

I es

=

ML

=*

Ta =pri

(P Vp x

-d = Vp =

x

x

= =

=

M

Mor =

To = M

g

Tro BM( +

=

2 VVV"

Vi MgY Vo

Vop

v + +

-

= = (x)]

a)

(P-Al (((anDe

((A (Per)

a (p

= - -

=

-

- - -p

Mod -In

V +

=

m

3 S

Muse

2x

= Mgsug 50

Mg

2x 0 x

= =

- =

-

j

BMgtit-Myxcop

Bigrit-Myx

V e =

BLamp-lepsing

Sostituisco x nella seconda equazione: =

leo-cop) Pe

Lend

0 & i

d

=

= = = .

p Arres

cost 1

B B =

By

1 a

=

=

= =

= Anop)

tro, di kari

Anp)

ap (0

(+ )

: ;

; 0 + -

=

.

, 1]

Vp(0

Ap ,

A

=M BigpMM

Cajxrip]

le Mglung

B = p Bigdcop +

&M

Rol)

B(x) Ne

po A

= -Mgl]

(Mg

B(x2 8 IBCO metheir

=

, -Agl BMgL

- I

B(x

B(xs )

83) Bar

-Ese

2Mg MgLB

0 sog

+, =

+

= =

, BingL 21 (1-B

MgLD +

5 3

B = M

= p

3x

(B(x 01))

XA(x1

01) 0

DET =

-

,, , (3) -33g-c-

deT)/2M8 Mo =

-

2 g

+

-72g2

*

Agl 13g

te 9 + +

+

= 622

A

We =

=

Wa

1 d

(B L(01

(B Snea

a) (A

A) L(sing Pale

+

+ +

=

- = - - cos

-

(B- A) Lande-Lestes

=

((sn81 sPz)

X +

= L(201 8)

y3 +

-

=

2 Pre

Asta &A

· w ;

=

M

. 11 Mi

Te I w =

Punto B

· E si)

L(081 (si

002)

B

UB 0 +

+

- =

= +

L(

(OisPi 20suitsi

este) (Disupe ++

++ +L 01)]

200 (0

= 20 +

= -

Moto IMl" a -Pl

To +

=I +

2 ( Q M

20012-p) M ( (0-0

1M 1ML +

=E

Ta

Tro To + +

+ +

+

= = 2

V -mag - maggi +

= -Mg(Leop Lampe

mogy +

- = Mg(t

magy =

- - Lespel 1k2"(1 20s(8-8)]

Long)]

1k 1k[)Lepe (ape +

+

= +

+ =

22 2

( -ll

+K

V -MgLaPe-MgLe +

=

3 Kilo-R

= -

MgLa +

Mglan-KLE-

= (0 i)

(it

it)

(0

a

Configurazioni di equilibrio: (it d

; ;

; ;

; , ,

Mg-K) Kill

=

KLandante

d'V KL"

reg sede

+

=

OndBe

↓ (Mgl-Ki-Kl

=

)Mgl-Ki) ed I

kirtriva KiritritkLe

+

H = (MgL-Klicle-Klamdisne

KLanGe KL"

ange reg sede

+

.

IH10 olk &

, po

↳

I Mgl-ki

k)2 Mgl k(2

-

ESAME 3/7/23

1 Te

T = +Marrone

=

2 V 1

V

V +

+

=

: 10x

v

V EMgRSO

=

V / 2xcord 1x Ax

+

. =

IMgraup-Myxo

3 Mex

V = -

3

S -Mgroppa

29 su

-MykpMgringerepthesp = 14

S

3 3

Assa(34)xz

De 3649

83

Tra

0

X1 = = = 9

VL 6

82 T/2

0

X2 = -

= Ot P3 Xz

I- X3

-

=

=

A

MinMyxMyri

= d

Mgrig

M

B Mysig permata

blade se

- sta

(51)

B(

B(xPl =

= a)

10 6 mot

-

(3 (xa

03) pa) La

Stabili se

e

, ,

?

5

ESAME 19/7/23

1 Ti +10

T +

= Up 5

P -

S

O V

- =

= =

T MorpMs

1

=

T 1 Mr MI

+ .

= 58'

1M(5

EMl

T +

= +

T 2

2 Vi vk

+

V V

+ +

=

=

V Mgs so

-

V 1 EML0

.

= - 2

=

V 1

-Mgscap-Mglsup

= +

3 La

10jss

Morp

= + =

de -A

Musimpos

= =

x

(5 i -

00

=

0 =

= =

=

A 3 tempo)

= or i

-Mi

= Museo

85201-9Orp Hopk vi

85282900 p Eye wo

B( Aer

BI5 8) :

=

.

5 M

= t

A

M

=

-

ESAME 27/2/24 of

1 To

Ti

T +

= REM

Fo =L M .

: Sol M

Irr

I 21

+ .

= =

↓

3 (2212

T . M1M

=1

1 I

= 2

P-0 2 ResDex-ZRsiPey-SesPex-ssinPer

= Gretex-ssirPey-s

-2REsinDex-2RErstex-SesPex Oper

= S

+

128 58

5

Vo 1258

+

+ +

=

T 1M(128 1250)

+

5

1 Mr 58

+ +

= = 2

2

Tezmrösötzurs