Dynamics 2 Flashcards
(11 cards)
1
Q
EOM for a linear undamped oscillating system
A
m x’’ + k x = 0
2
Q
EOM for a rotational undamped oscillating system
A
IG θ’’ + kθ θ = 0
3
Q
EOM for linear damped oscillating system
A
m x’’ + c x’ + k x = 0
4
Q
EOM for linear damped forced oscillating system
A
m x’’ + c x’ + k x = F(t)
5
Q
Frequency ratio r
A
r = ω / ωn
6
Q
Maximum amplitude response frequency
A
ωmax = ωn sqrt( 1 - 2ζ2 )
For low damping, basically the same as ωn
7
Q
Out of Balance Oscillating Excitation Force
A
Fexi = m’ r ω2 sin(ωt)
8
Q
Forces for Phasor Diagrams
A
Inertia: m ω2 x0 (-90 from damping)
Damping: c ω x0 (-90 from spring)
Restoring spring: k x0 (-φ from force)
9
Q
Force transmitted to ground
A
FT = k x+ c x’
(Spring and damping, not inertia)
10
Q
Max Force on Ground
A
FT,max = x0 sqrt( k2 + (cω)2 )
11
Q
A
