Ejercicio N° 01 Delta T = 0.1

7/26/2019 Ejercicio N 01 Delta T = 0.1

1/34

6/11/2016Ejercicio N 01

Un sistema de un grado de libertad lineal elstico est dado en la

1.00 Seg

m = 1.00 Kg

5.00%

g = 9.1 m!s"#ondiciones iniciales:

0.00

0.00

gr$ico, use t = 0.10 Seg

m 0.5

i = 0 i = 1 i = & i = ' i = (

0.1 0.& 0.' 0.(

0.5

SOLUCINAlgortmo de iteracci!

1.00

m = 1.00 Kg t = 0.10 Seg

& ) '.1(1* ! 1Seg

6"2#$2 %rad/&eg'

+ = 1Kg ) *.&'&" rad!seg-"

+ = '9.( Kg!seg"./m!m-

( )$*"+,# %N/m'

c =& ) 1Kg ) 0.05 ) *.&'&rad!seg

c = 0.*&'& Kg!seg./m!m./seg!seg-

c ) 0"62#$2 %N"&eg/m'2.00

esconocido

0.00

0.00

0.00

Si i = 0

2n=

=

u0=

30=

etermine la res4uesta de des4laamiento u/t

debido a la e)citaci6n

7g/g

Defnir m, c, k, u0,

0, F

i= F(t

i) y t

=8

n

=

-)

m + c + ku = F(t)

m7i c3

i +u

i= /t

i =

i

7i= 7/t

i = 7

0=

3i= 3/t

i = 3

0=

ui= u/t

i = u

0=

/ti =

0=

=&

_

/_

"=._

=& .. ._

7;0= ;0


2/34

0 /0.*&' ) 0 /'9.( ) 0- ! 1

0.00 m!s"-

3.00Clculo e k!

+> = '9.( /&)0.*&'!0.1 /()1!0.1"

(. )+2"0+ %N/m'

".00 i # i+1$.00

?ara i = 0

o> = @o /()1!0.1&)0.*&'&-)0 &)1)0

o> = 0 0.000

0.000

0.5.g 0

o> =1)0.5)9.1 0

o. )+"*0 N

%.00(.905!(5&.0(5

0"010* m

&.00

?ara i = 0

/&!0.1)0.0109 &)0

0"21, m/&

?ara i = 0

/()0.0109!0.1" /()0!0.1 &)0

+"$+0 m/&3

'.00

70=

70=

Clculo e Fi!

/t = m.7g/t

i = i1

i= /t

i1 /t

i

= m7g/t

i1 m7

g/t

i

= m/7gi1

7gi

i = m7gi

o> = m.7gi= m./7

gi1 7

gi

o> = m.7gi= m.

Determinmo* ui= Fi!ki!u

0=

40)

Clculmo iy

i

30=

50)

70=

0)

ui+1

= ui+ u

i

i+1=

i+

i

u01

= u0 u

0 3

01= 3

0 3

0

; =

+. )

Determinmo* ui= F

i!k

i!

u(=

4+)

Clculmo iy

i

3(

=

5+)

7(=

+)

ui+1

= ui+ u

i

i+1=

i+

i

4) 5

)

)

Clculo e Fi!

5> =

. )

Determinmo* ui= F

i!k

i!

u5=

4)

Clculmo iy

i

35=


5/34

0"00 m/&

/()0.1(11!0.1" /()1.1*!0.1 /&)5.(9&

0"*,# m/&3

'.00

0"$62 m 1"661 m/&

.00 -etornr l o n/mero ".00

".00 i = %

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)1.**1 &)1)(

#2"++# N

%.00

&.((5!(5&.0(5

0"1#2+ m

&.00

/&!0.1)0.1&( &)1.**1

0"$26 m/&

/()0.1&(!0.1" /()1.**1!0.1 /&)(.515

2"01 m/&3

'.00

0"$#6 m 1"*#, m/&


".00 i = &$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)1.9 &)1)&

*0"*1+ N

%.00

90.91(5!(5&.0(5

0"2011 m

&.00

/&!0.1)0.&011 &)1.9

0"0+# m/&/()0.&011!0.1" /()1.9!0.1 /&)&.01(

$"06 m/&3

'.00

0",$*, m 2"0$ m/&


5)

75=

)

ui+1

= ui+ u

i

i+1=

i+

i

46) 56) 6)

Clculo e Fi!

*> =

6. )

Determinmo* ui= F

i!k

i!

u*=

46)

Clculmo iy i3

*=

56)

7*=

6)

ui+1

= ui+ u

i

i+1=

i+

i

4,) 5

,)

,)

Clculo e Fi!

> =

,. )

Determinmo* ui= F

i!k

i!

u=

4,)

Clculmo iy

i

3=

5,)7

=

,)

ui+1

= ui+ u

i

i+1=

i+

i

4#) 5

#)

#)


6/34

".00 i = '

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)&.0'5 &)1)1.

#6",,0 N

%.00

*.05!(5&.0(50"1*20 m

&.00

/&!0.1)0.19& &)&.0'5

0"2$1 m/&

/()0.19&!0.1" /()&.0'5!0.1 /&)1.051

2"2, m/&3

'.00

0"*$1, m 1"#0+ m/&


".00 i =

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)1.0( &)1)'.

,2"162 N

%.00

&.1*5&!(5&.0(5

0"1*6 m

&.00

/&!0.1)0.159* &)1.0(

0"+1 m/&

/()0.159*!0.1" /()1.0(!0.1 /&)'.59

1"1$, m/&3

'.00

1"0*1$ m 1"$#* m/&


".00 i = 10

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)1.'9 &)1)(.

2",#2$ N

%.00

5&.&'!(5&.0(5

0"116# m

&.00

Clculo e Fi!

> =

#. )

Determinmo* ui= F

i!k

i!

u

=

4#)

Clculmo iy

i

3=

5#)

7=

#)

ui+1

= ui+ u

i

i+1=

i+

i

4*) 5

*)

*)

Clculo e Fi!

9> =

*. )

Determinmo* ui= F

i!k

i!

u9=

4*)

Clculmo iy

i

39=

5*)

79=

*)

ui+1

= ui+ u

i

i+1=

i+

i

410

) 510

) 10

)

Clculo e Fi!

10> =

10

. )

Determinmo* ui= F

i!k

i!

u10

=

410

)

Clculmo iy

i


7/34

/&!0.1)0.11* &)1.'9

0"++$ m/&

/()0.11*!0.1" /()1.'9!0.1 /&)(.15

0",+ m/&3

'.00

1"20#1 m 0"*+6 m/&.00 -etornr l o n/mero ".00

".00 i = 11

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)0.9(* &)1)(.

$"6# N

%.00

'5.*55!(5&.0(5

0"0,#* m

&.00

/&!0.1)0.09 &)0.9(*

0"$1 m/&

/()0.09!0.1" /()0.9(*!0.1 /&)(.1(&

1"*#* m/&3

'.00

1"2#6* m 0"6$1 m/&


".00 i = 12

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)0.*'1 &)1)&.

26"601 N

%.00

&*.*501!(5&.0(5

0"0*0 m

&.00

/&!0.1)0.059 &)0.*'1

0"0#+ m/&

/()0.059!0.1" /()0.*'1!0.1 /&)&.15'

2"6$0 m/&3

'.00

1"$+* m 0"+# m/&


310

=

510

)

710

=

10

)

ui+1

= ui+ u

i

i+1=

i+

i

411) 511) 11)

Clculo e Fi!

11

> =

11

. )

Determinmo* ui= F

i!k

i!

u11

=

411

)

Clculmo iy

i

311

=

511

)

711

=

11

)

ui+1

= ui+ u

i

i+1=

i+

i

412

) 512

) 12

)

Clculo e Fi!

1&

> =

12

. )

Determinmo* ui= F

i!k

i!

u1&

=

412

)

Clculmo iy

i

31&

=

512)

71&

=

12

)

ui+1

= ui+ u

i

i+1=

i+

i

41$

) 51$

) 1$

)


8/34

".00 i = 13

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)0.5( &)1)0

2#"+2# N

%.00

&.(5&!(5&.0(50"062* m

&.00

/&!0.1)0.0*&9 &)0.5(

0"16+ m/&

/()0.0*&9!0.1" /()0.5(!0.1 /&)0.(

2"$1, m/&3

'.00

1"+0## m 0",11 m/&


".00 i = 1"

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)0.11 &)1)&

$*"#$# N

%.00

'9.'5!(5&.0(5

0"0##1 m

&.00

/&!0.1)0.01 &)0.11

0"$+0 m/&

/()0.01!0.1" /()0.11!0.1 /&)&.9(

1"212 m/&3

'.00

1"+*,0 m 1"01 m/&


".00 i = 1$

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)1.051 &)1)(

6"2*00 N

%.00

5*.&9!(5&.0(5

0"12+ m

&.00

Clculo e Fi!

1'

> =

1$

. )

Determinmo* ui= F

i!k

i!

u1'

=

41$

)

Clculmo iy

i

31'

=

51$

)

71'

=

1$

)

ui+1

= ui+ u

i

i+1=

i+

i

41+

) 51+

) 1+

)

Clculo e Fi!

1(

> =

1+

. )

Determinmo* ui= F

i!k

i!

u1(

=

41+

)

Clculmo iy

i

31(

=

51+

)

71(

=

1+

)

ui+1

= ui+ u

i

i+1=

i+

i

41

) 51

) 1

)

Clculo e Fi!

15> =

1

. )

Determinmo* ui= F

i!k

i!

u15

=

41

)

Clculmo iy

i


9/34

/&!0.1)0.1&(5 &)1.051

0"$## m/&

/()0.1&(5!0.1" /()1.051!0.1 /&)(.00

0"2 m/&3

'.00

1"621 m 1"+$* m/&.00 -etornr l o n/mero ".00

".00 i = 1%

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)1.('9 &)1)'

,1",# N

%.00

1.55!(5&.0(5

0"1## m

&.00

/&!0.1)0.15 &)1.('9

0"2*# m/&

/()0.15!0.1" /()1.('9!0.1 /&)'.5&

1"1 m/&3

'.00

1",#0$ m 1",$, m/&


".00 i = 1&

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)1.' &)1)&

#0"*62 N

%.00

0.9*&5!(5&.0(5

0"1,*1 m

&.00

/&!0.1)0.191 &)1.'

0"10# m/&

/()0.191!0.1" /()1.'!0.1 /&)&.&01

2"2$+ m/&3

'.00

1"**+ m 1"#+ m/&


315

=

51

)

715

=

1

)

ui+1

= ui+ u

i

i+1=

i+

i

416) 516) 16)

Clculo e Fi!

1*

> =

16

. )

Determinmo* ui= F

i!k

i!

u1*

=

416

)

Clculmo iy

i

31*

=

516

)

71*

=

16

)

ui+1

= ui+ u

i

i+1=

i+

i

41,

) 51,

) 1,

)

Clculo e Fi!

1

> =

1,

. )

Determinmo* ui= F

i!k

i!

u1

=

41,

)

Clculmo iy

i

31

=

51,)

71

=

1,

)

ui+1

= ui+ u

i

i+1=

i+

i

41#

) 51#

) 1#

)


10/34

".00 i = 1'

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)1.(5 &)1)0.

#0"*66 N

%.00

0.9**5!(5&.0(50"1,*1 m

&.00

/&!0.1)0.191 &)1.(5

0"10# m/&

/()0.191!0.1" /()1.(5!0.1 /&)0.0''

2"0*# m/&3

'.00

2"1$# m 1",$, m/&


".00 i = 1

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)1.' &)1)&.

,2"$061 N

%.00

&.'0*1!(5&.0(5

0"1600 m

&.00

/&!0.1)0.1* &)1.'

0"2, m/&

/()0.1*!0.1" /()1.'!0.1 /&)&.1'1

1"2$, m/&3

'.00

2"2*# m 1"+62 m/&


".00 i = 20

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)1.(*& &)1)'.

#"+##$ N

%.00

5.('!(5&.0(5

0"12*+ m

&.00

Clculo e Fi!

1

> =

1#

. )

Determinmo* ui= F

i!k

i!

u1

=

41#

)

Clculmo iy

i

31

=

51#

)

71

=

1#

)

ui+1

= ui+ u

i

i+1=

i+

i

41*

) 51*

) 1*

)

Clculo e Fi!

19

> =

1*

. )

Determinmo* ui= F

i!k

i!

u19

=

41*

)

Clculmo iy

i

319

=

51*

)

719

=

1*

)

ui+1

= ui+ u

i

i+1=

i+

i

420

) 520

) 20

)

Clculo e Fi!

&0> =

20

. )

Determinmo* ui= F

i!k

i!

u&0

=

420

)

Clculmo iy

i


11/34

/&!0.1)0.1&9( &)1.(*&

0"$$6 m/&

/()0.1&9(!0.1" /()1.(*&!0.1 /&)'.'*

0"00# m/&3

'.00

2"+2,# m 1"126 m/&.00 -etornr l o n/mero ".00

".00 i = 21

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)1.1&* &)1)'.

++"62,0 N

%.00

((.*&!(5&.0(5

0"0*#, m

&.00

/&!0.1)0.09 &)1.1&*

0"2,, m/&

/()0.09!0.1" /()1.1&*!0.1 /&)'.'*

1"1#2 m/&3

'.00

2"266 m 0"#+* m/&


".00 i = 22

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)0.(9 &)1)&.

$"66, N

%.00

'5.5**!(5&.0(5

0"0,#, m

&.00

/&!0.1)0.0 &)0.(9

0"12+ m/&

/()0.0!0.1" /()0.(9!0.1 /&)&.1

1"#,, m/&3

'.00

2"602 m 0",2 m/&


3&0

=

520

)

7&0

=

20

)

ui+1

= ui+ u

i

i+1=

i+

i

421) 521) 21)

Clculo e Fi!

&1

> =

21

. )

Determinmo* ui= F

i!k

i!

u&1

=

421

)

Clculmo iy

i

3&1

=

521

)

7&1

=

21

)

ui+1

= ui+ u

i

i+1=

i+

i

422

) 522

) 22

)

Clculo e Fi!

&&

> =

22

. )

Determinmo* ui= F

i!k

i!

u&&

=

422

)

Clculmo iy

i

3&&

=

522)

7&&

=

22

)

ui+1

= ui+ u

i

i+1=

i+

i

42$

) 52$

) 2$

)


12/34

".00 i = 23

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)0.&5 &)1)0.

$+"20 N

%.00

'(.&055!(5&.0(50"0,, m

&.00

/&!0.1)0.05 &)0.&5

0"06+ m/&

/()0.05!0.1" /()0.&5!0.1 /&)0.'01

1"#,# m/&3

'.00

2"6#0* m 0",#* m/&


".00 i = 2"

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)0.9 &)1)1

+0"*10 N

%.00

(0.591!(5&.0(5

0"0#*# m

&.00

/&!0.1)0.09 &)0.9

0"21* m/&

/()0.09!0.1" /()0.9!0.1 /&)1.5*

1"22$ m/&3

'.00

2",,0, m 1"00, m/&


".00 i = 2$

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)1.00 &)1)&

2"061, N

%.00

5&.0*1!(5&.0(5

0"112 m

&.00

Clculo e Fi!

&'

> =

2$

. )

Determinmo* ui= F

i!k

i!

u&'

=

42$

)

Clculmo iy

i

3&'

=

52$

)

7&'

=

2$

)

ui+1

= ui+ u

i

i+1=

i+

i

42+

) 52+

) 2+

)

Clculo e Fi!

&(

> =

2+

. )

Determinmo* ui= F

i!k

i!

u&(

=

42+

)

Clculmo iy

i

3&(

=

52+

)

7&(

=

2+

)

ui+1

= ui+ u

i

i+1=

i+

i

42

) 52

) 2

)

Clculo e Fi!

&5> =

2

. )

Determinmo* ui= F

i!k

i!

u&5

=

42

)

Clculmo iy

i


13/34

/&!0.1)0.115& &)1.00

0"2#* m/&

/()0.115&!0.1" /()1.00!0.1 /&)&.99

0"1,, m/&3

'.00

2"##* m 1"2*6 m/&.00 -etornr l o n/mero ".00

".00 i = 2%

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)1.&9* &)1)&

6+"$2,# N

%.00

*(.'&!(5&.0(5

0"1+2$ m

&.00

/&!0.1)0.1(&' &)1.&9*

0"2+ m/&

/()0.1(&'!0.1" /()1.&9*!0.1 /&)&.9*

0"#,$ m/&3

'.00

$"02#2 m 1"0 m/&


".00 i = 2&

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)1.55 &)1)&.

,$"0602 N

%.00

'.0*0&!(5&.0(5

0"1616 m

&.00

/&!0.1)0.1*1* &)1.55

0"1$2 m/&

/()0.1*1*!0.1" /()1.55!0.1 /&)&.10'

1"* m/&3

'.00

$"1#*# m 1"6#2 m/&


3&5

=

52

)

7&5

=

2

)

ui+1

= ui+ u

i

i+1=

i+

i

426) 526) 26)

Clculo e Fi!

&*

> =

26

. )

Determinmo* ui= F

i!k

i!

u&*

=

426

)

Clculmo iy

i

3&*

=

526

)

7&*

=

26

)

ui+1

= ui+ u

i

i+1=

i+

i

42,

) 52,

) 2,

)

Clculo e Fi!

&

> =

2,

. )

Determinmo* ui= F

i!k

i!

u&

=

42,

)

Clculmo iy

i

3&

=

52,)

7&

=

2,

)

ui+1

= ui+ u

i

i+1=

i+

i

42#

) 52#

) 2#

)


14/34

".00 i = 2'

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)1.*& &)1)0

,"+0+* N

%.00

5.(0(9!(5&.0(50"166# m

&.00

/&!0.1)0.1** &)1.*&

0"02* m/&

/()0.1**!0.1" /()1.*&!0.1 /&)0.5(5

1"662 m/&3

'.00

$"$66 m 1"6+ m/&


".00 i = 2

$.00

1)/00)9.1 /()1!0.1&)0.*&'&-)1.*5( &)1)1.

,0"#*,# N

%.00

0.9!(5&.0(5

0"16# m

&.00

/&!0.1)0.15* &)1.*5(

0"1,1 m/&

/()0.15*!0.1" /()1.*5(!0.1 /&)1.11

1"1,* m/&3

'.00

$"1$+ m 1"+#$ m/&


Clculo e Fi!

&

> =

2#

. )

Determinmo* ui= F

i!k

i!

u&

=

42#

)

Clculmo iy

i

3&

=

52#

)

7&

=

2#

)

ui+1

= ui+ u

i

i+1=

i+

i

42*

) 52*

) 2*

)

Clculo e Fi!

&9

> =

2*

. )

Determinmo* ui= F

i!k

i!

u&9

=

42*#

)

Clculmo iy

i

3&9

=

52*

)

7&9

=

2*

)

ui+1

= ui+ u

i

i+1=

i+

i

4$0

) 5$0

) $0

)


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fgura que se muestra, con:

i = 5

0.5

5.00%

en la base 7/g

defnido en el


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i+1=

i+

i

01= 7

0 7

0


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0 (.'(

+"$+0 m/&3

(.'(

1",# m/&3

1.5

1",,# m/&3

i+1=

i+

i

i+1=

i+

i


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1.

+"+*6 m/&3

.(9*

"+*2 m/&3

9&

i+1=

i+

i

i+1=

i+

i


19/34

+"1 m/&3

.515

2"01+ m/&3

.01(

1"01 m/&3

i+1=

i+

i

i+1=

i+

i

i+1=

i+

i


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51

$",* m/&3

9

+",1 m/&3

15

i+1=

i+

i

i+1=

i+

i


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+"1+2 m/&3

1(&

2"1$ m/&3

15'

0"+,, m/&3

i+1=

i+

i

i+1=

i+

i

i+1=

i+

i


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.(

2",*+ m/&3

.9(

+"00, m/&3

.00

i+1=

i+

i

i+1=

i+

i


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$",2 m/&3

.5&

2"201 m/&3

.&01

0"0$$ m/&3

i+1=

i+

i

i+1=

i+

i

i+1=

i+

i


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''

2"1$1 m/&3

1'1

$"$6# m/&3

*

i+1=

i+

i

i+1=

i+

i


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$"$60 m/&3

*

2"1,# m/&3

1

0"$01 m/&3

i+1=

i+

i

i+1=

i+

i

i+1=

i+

i


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01

1",6 m/&3

.5*

2",** m/&3

.99

i+1=

i+

i

i+1=

i+

i


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2"*,6 m/&3

.9*

2"10$ m/&3

0'

0"+ m/&3

i+1=

i+

i

i+1=

i+

i

i+1=

i+

i


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.5(5

1"11# m/&3

11

2"2*, m/&3

i+1=

i+

i

i+1=

i+

i


29/34

6/11/2016?ara t = 0.100 Segundos

i

0 0 0.0000 0.000 0.000

1 0.10 0.0109 0.&1 (.'(0

& 0.&0 0.0'90 0.'(* 1.5

' 0.'0 0.0' 0.'( 1.( 0.(0 0.1&(1 0.**1 (.(9*

5 0.50 0.&151 1.1*0 5.(9&

* 0.*0 0.'5*& 1.**1 (.515

0.0 0.5'* 1.9 &.01(

0.0 0.'9 &.0'5 1.051

9 0.90 0.9'1 1.0( '.59

10 1.00 1.091' 1.'9 (.15

11 1.10 1.&01 0.9(* (.1(&

1& 1.&0 1.&*9 0.*'1 &.15'

1' 1.'0 1.'(59 0.5( 0.(1( 1.(0 1.(0 0.11 &.9(

15 1.50 1.(90 1.051 (.00

1* 1.*0 1.*&15 1.('9 '.5&

1 1.0 1.0' 1.' &.&01

1 1.0 1.959( 1.(5 0.0''

19 1.90 &.1'5 1.' &.1'1

&0 &.00 &.&95 1.(*& '.'*

&1 &.10 &.(& 1.1&* '.'*0

&& &.&0 &.5&** 0.(9 &.1

&' &.'0 &.*05& 0.&5 0.'01&( &.(0 &.*09 0.9 1.5*

&5 &.50 &.0 1.00 &.99

&* &.*0 &.59 1.&9* &.9*

& &.0 '.0&& 1.550 &.10'

& &.0 '.19 1.*& 0.5(5

&9 &.90 '.'5** 1.*5( 1.11

'0 '.00 '.51'( 1.(' &.&9

ti

ui

3i

i

DEFGHIF1HI:


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0 0.5 1

-8

-6

-4

-2

0

2

4

6

Grfico: Aceleraci

Aceleracin ( [m/s])

0 0.5 1

-4

-4

-3

-3

-2

-2

-1

-1

0

Grfico: Desplazamie

Desplazamiento (u [m])

0 0.5 1

-3

-2

-2

-1

-1

0

Grfico: Velocidad

T

Velocidad ( [m/s])


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1.5 2 2.5 3

Vs. Tiempo ( - t)

1.5 2 2.5 3

to Vs. Tiempo (u - t)

Tiempo (t [Segundos])

1.5 2 2.5 3

Vs. Tiempo (u - t)

empo (t [Segundos])


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Ejercicio N° 01 Delta T = 0.1

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Transcript of Ejercicio N° 01 Delta T = 0.1