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System Dynamics Reference Sheet

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System Dynamics
Reference sheet
Definitions
ofa
Amplitude body
from
itsequilibriumposition
displacement
maximum
vibration age.at
Degrees Freedom
Freevibration
Forcedvibration
Harmonic
motion
of
Period oscillation
e
timetarentocompleteonecycleotmotion
where warantreavenscrain
thaterepeatsitseitatteran
Oof
of
vibrating
toof the
minimum
Frequency
independent
coordinates
of
required determine
p osition
aupartsotasys.atany
instant
of
oscillation
f
oscillates itself
afteran
sys
byavoexternacorces
initialdisturbance
an
repeating
Enesco
unit
cites
time
of per
cycles
t
t E
external
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is
e quilibrium
positionotmassm
the
motion
about
that symmetric
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i aignesit
combiningsprings
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a
n
it
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Free Vibration W
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combining Dampers
parallelvampers
series vampers
m
rs.int
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Viscous Damping
where
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where
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SOF systems
case 3
Overdamped system
tozero
eventually diminishes
Y 1 or c cc
solution
xcts aetstistswnttc.ec
where
solution
G
xces
x.cocane
town
8 In
ForsmallDamping gez.TT if Jet
isanotherformofthe dampingRatio g
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IF
I
s
If smalldamping
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to
timet
amplitude
corresponding
ti
S
21T
Ye Janta Jun I yea ZTT
age
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any
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Logarithmic Decrement
s ustwnt
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s 1min
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In
are
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x
2 Torsional System
Free vibration Novamping
o
g
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if
on
Mo Gato owhere
argue
Torsional
spring
constant
m
I
athaceabstone
KEMI GE nad
Eyofmotion Jo k 0 0
where
Jon strong
Oct Acoscont Asinant
solution
Art
AiGolan
Natural
circular
Frey
E
Istrati
Response
VE
n 2
of
Fg
Period
vibration
Wn
FE
of FirstorderSys s Timeconstant
ExtTorqueo
Assuming
Ctw O
EFI Jaiwhere
J they
of
EYBEARY
cod
velocity
angular
w
cerateotchangeot
solution
Free Vibration W
viscousdamping
torque
T
velocity
angular
wet woe
0.308Wo
timeconstant e
E
Viscous Damping
Ct
where
where
Joey
keg
o
Cotyp
É giggayot
JOtc K O
Eqof
motion
I
the
moreof
Effacement
displacement
angular
wa V1 g an
ofdumped
freq
vibration
where
wat
S
ft
E Iw
Ce
zero
torsional
damping
catfish
Solution
sameasFreevibrationw damping springmass
ICI
cases underdampet
or acca
too
oct E esasinwat
oiwiteitzo.o.su
where
w
Ortan 8Yano
or
Oct eswiftcos
wattoot noo sina.at
9 1 or aces
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case3 overdamped
I 1 or Ceetc
ifwng.ecsve isat
aces aetstt
case2
d umped
critically
Oct
where
a
a
town stir
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zanies
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a
Free vibration nodamping
I TKO O
Forcedvibrations of SOOF Systems
o
NODAMPING
Forced vibrations W
of
Eg
motion
m
MY Kx
Generalsoli
Focoswt
n
Xlt XnCttXpCt
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m
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of
Eg
motion
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ifjjjj
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son
cosat
Focoswt
kmas tear t
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an't
TotalSol'n
Amplificationmanification
Factor
Act Xo Emacount
M
É
I
sinant Imancoset
Amplification
M
Factor
ATRESONANCE
where r
En
E 5 25 7
ri
agr
freqratio
xctsx.tn
Ioéswntcos
ÉtÉÉ
using
r
xct
Is
ra
wat do
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where
TotalResponse
1
1
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1
mm
1
É
I
Xocosconttig sinant
w un
Wa
Io
stuntsinant
Beating
Fun
so w sing
xo IcosojtwtlswnxotioJw.I.co
WaXo I cosy
critically
of
The
sameideaworks
fortheothercases
m
xct
simplifiedsolin
mm
I Mw
dumped
systemsxcesxncestx.ca
T
periodof
beating a
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overdanped
coswtcosw.tl
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pitied
o
wing
whereesmall
positions
Iw
w
freqof
as Wb Ze an w
beating
forced vibrations wanoamen
mm
of Mit CI thx Feint
Eg
Motion
k a
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m
Feint
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Xnct xpCt
e
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Response
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at
where
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Fo
x mortem't
tan
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complex
Number
Im n
y
System Review
it xtiy
90
to
Cartesian
z
r
a
Re
ECKEY
p anglephase
xtiy
genpoint
complex
conjugate
polar
rcoso
iprising
r
xity
Atan Y
Z r cosotising
reid
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