(c)2017 Second Wind Productions, LLC
Here Here is our our frst frst o two two mobile mobile probl problems. ems. The weig weights hts are are based based o rod lengths lengths are based on a Fibanocci Fibanocci Sequence. Sequence. Type in values o o Set up and solve it as we have done. "emember to shade your m
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
n a geometric progression, while the [! and ["!, as applicable.
trices# [S! values in ractional orm. orm .
d$
d%
d&
d'
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
32
-32
0
0
0
0
16
-16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
[(! d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12
(c)2017 Second Wind Productions, LLC
=
(c)2017 Second Wind Productions, LLC
[!
[(!
d)
d*
d+
d
d-
d$
d$$
d
%$0
0
0
0
0
0
0
0
d1
0
0
0
0
0
0
0
0
d2
1
1
0
0
0
0
0
0
d3
0
0
1
1
0
0
0
0
d4
0
0
0
0
1
1
0
0
d5
0
0
0
0
0
0
1
1
d6
0
0
0
0
0
0
0
0
d7
0
0
0
0
0
0
0
0
d8
8
-8
0
0
0
0
0
0
d9
0
0
4
-4
0
0
0
0
d10
0
0
0
0
2
-2
0
0
d11
0
0
0
0
0
0
1
-1
d12
[S! 10
1 2
10
1 2
6
1 2
6
1 2
4 4 2
1 2
2
1 2
1
1 2
1
1 2
1 1
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
["! 21 13 8 5 3 =
2 0 0 0 0 0 0
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
nce calculated, you will use these values to determine the overall lateral circular beam along with the distance, d, to the let o the pivot point. ?ust ollow my lead below on how to solve or this @artsy@ system
2A" A;:TS >F 95" 2 $BB 9a3e sure to select <44 values or the ormulae and mat 5(5"=TH:;C Dall valuesE that you need to use are ound in a cell on
Here is the ormula or determining the de/ection Solving or 2$0 W Here, 5 is called the Modulus of Elasticity , while I is the
Here are your parameters# you will select these cells as needed0
I 8
+1-
alculate the 9oment o :
2$ 8
-%.
alculate the value o 2 $
pounds
;ow let6s calculate 2%# this is a donated bloc3 o granite, and its value is gi
2e are now ready to solve or our un3nowns, d and 40 Here are our distance and balance equations0
L
=
20
W 2 d
(c)2017 Second Wind Productions, LLC
=
+
d
20W 1
(c)2017 Second Wind Productions, LLC
[!
[(!
d
4
-1
1
["!
d % = 27!7 0 4 % Remember to not type in any values (see above! This includes the labels for your unknowns along Colum
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
ective techniques that eeded at the right u will have to also length, 4, o the
ices# this wor3sheet.
a beam0
δ
=
WL3 3 EI
3 EI δ L3
beam6s Moment of Inertia# I is a unction o the beam6s cross7section a 5 DpsiE
DinE
&.5+
4 DtE
r DinE
$ % $ ther values to be selected
0
1
3
3!142
DG1t&E
(2% Dt&E
$+
$)
4
12
ertia here# epress as a raction Dto one digitE
ere# epress to $ decimal place# watch your units when entering 4B
en as0 2% 8
W 2
%)). pounds
=
V γ
8 density I ( 8 volume
alculate the value o 2 % here to $ decimal plac that unit conversions are not needed hereJ
>bviously, we are going to have to do some @algebra frst@ on the dista
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
[(! d 4
[S! .+ %.+ feet (" decimal place
=
n E!
(c)2017 Second Wind Productions, LLC
=
Convert t
(c)2017 Second Wind Productions, LLC
d is determined by0
I =
π
4
r 4
# note
ce equation beore we can enter its values below . . .
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
[S! .+ %'.+ inches (" decimal
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
f ( x )
=
Ax 6
+
Bx 5
+
Cx 4
+
Dx 3
+
Ex 2
+
Fx
+
Set up using :F5"">" and fnish this system as we did i =>A 9AST AS5 )& )' )" * " ' &
#
$
%
'
"
& [! M
<
L
5
F
729
-243
81
-27
9
-3
64
-32
16
-8
4
-2
1
-1
1
-1
1
-1
0
0
0
0
0
0
1
1
1
1
1
1
64
32
16
8
4
2
729
243
81
27
9
3
+ou shade in per your choi
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
the K<# remember to shade in your matrices average o data values
* [(!
["!
C 1
"
810!1
1
#
88!5
1
C
6!0
1
$
1
%
-0!7
1
&
42!3
1
'
651!6
=
1!8
-*% -. $ " )" %% #$/
-*. -# & )" %& #%-
-"/ .* / ' * %' ##$
-"" -/ " )" %" #%"
f( -"/ .* # " )" %$ #$"
0ormatting [(!
[S!
"
1!0
#
0!0
C
0!0
$
=
-2!6
%
-0!2
&
-0!7
'
1!8
Type out the equation below w based on the applicable coeNc the let. =ou may use a O to re calculate D&E, either oPine or tet bo. DE 8 O*7%.*O&7.%O%7.+ D&E 8 *)*.+
3
e(s of color(s 6
1!0
5
0!0
4
0!0
3
-2!6
2
-0!2
1
-0!7
0
1!8
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
, -"% -/ % % * %' ##'
-*/ -# & )" %* #$-
-"* -/ " * %& #%$
-*& ." / " )" %* #$/
-*. -& " )" %& #&'
here indicated in this tet bo, ient values you have determined at present an eponent. Then in the space immediately below the
$.
729!0 0!0 0!0 -70!2 -1!8 -2!1 1!8 656!7
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
2e are going to determine the coeNcients or a rational uncti approach rom what we have been doing. Here is our unction0
R( x)
=
P ( x) Q( x)
=
c11 x c21 x
3
3
+
c12 x
2
+
c22 x
2
+
c13
+
c23
;ote that we have segregated our numera rom those o the denominator DRDEE. Thi equations or our un3nown coeNcients. 2e are going to program the [! and ["! per the below instructions .
Type in all s in ust the yellow7shaded cells in the 7matri. ;ow appropriately use the :F5"">" macro as you have been ta neededE in the two blue7shaded cells# remember to utilie by c values along olumn 9 and "ow %. ;et, type in the values or the "7matri based on the above Ase an appropriate macro to populate the (7matri, and then a where indicated at the upper right.
2atch your ormatting o your coe Then proceed to the tet bo at the upper right Dbelow our
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
n
n using a slightly diQerent
x
& ↓
$$ + +
c14
3(
c24
64
% ' )' )% & " * )%
4( tor6s DKDEE results s gives us unique
8 -8 -64 0 0 0 0
Type in each o the values in [S!# epr or in the space to t
atrices accordingly
ught Dincluding typing in a $ as ll reerence calls the applicable
boundary condition points. ppropriately solve or the S7matri
cient6s valuesBB matricesE or the remainder . . .
un
lim R ( x
x → ∞
.
*. 2hat is the ste
&
+. For what valueD
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
,
. For what valueD
(c)2017 Second Wind Productions, LLC
7'
(c)2017 Second Wind Productions, LLC
'
"
*
&
'
"
*
1C2
%$$&
$'
%$
%%
%&
%'
16
4
1
0
0
0
0
4
2
1
0
0
0
0
4
-2
1
0
0
0
0
16
-4
1
0
0
0
0
0
0
0
27
9
3
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
-64
16
-4
1
ollowing answers as and where indicated below. The questions ar ss all numerical values to $ decimal place. =ou may calculate thes he right o this tet bo.
Mo not elaborate# ust answer. $. "DE 8 U : it is undefned, then state so.
.
%. "D$E 8 U : it is undefned, then state so.
.
&. "D7&E 8 U : it is undefned, then state so.
.)
'. "D7'E 8 U : it is undefned, then state so.
efned =
?
dy state value o "DE, i any# i none, type in 56E.
E o is "DE 8 U : none, type in 56E.
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
E o is "DE undefnedU : none, type in 56E.
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
1R2
[(!
[S!
4
C11
0!0
-2
C12
1!0
10
C13
-3!0
28
C14
91
C21
65
C22
0!0
64
C23
0!0
0
C24
64!0
e based on your answers oPine,
=
0!0 1!0
;>T5B
7!73
P()
()
3
0!0
1!0
2
1!0
0!0
1
-3!0
0!0
0
0!0
64!0
SP()
S()
0!0
461!9
59!8
0!0
-23!2
0!0
0!0
64!0
36!6
525!9
0!1
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
(c)2017 Second Wind Productions, LLC
