Oscillations

Question 1

When is a set of coordinates q_j called complete

Answer 1

If q_j can localize the system at any time

Question 2

When is a set of coordinates q_j called independent?

Answer 2

If q_j for the only coordinate that is not fixed, there is the possibility of free changeability

Question 3

Are complete and independent sets of coordiates unique?

Answer 3

No

Question 4

What is the number of coordinates for a complete and independent set of coordinates?

Answer 4

Degree of freedom

Question 5

What is oscilation

Answer 5

Repetitive or periodic variation, typically in time of some measure about a central value

Question 6

What is periodic oscillation?

Answer 6

Oscillation that repeats exactly after time

Question 7

What is harmonic oscillation?

Answer 7

Oscillation for which there is only one frequency

Question 8

What is free oscillation?

Answer 8

Oscillation without an external force

Question 9

How are springs added in parallel?

Answer 9

1+2+3

Question 10

How are springs added in series?

Answer 10

1/1 + 1/2 + 1/3

Question 11

What are three sources of Damping?

Answer 11

Fluid drag
Coloumb / Dry Friction
Internal Damping

Question 12

What is the general equation of oscillation?

Answer 12

MX’’ + CX’ + KX = F

Question 13

What is F in the general oscillation equation?

Answer 13

K . x = f

Question 14

What is the damping matrix?

Answer 14

C

Question 15

What is the Stiffness Matrix?

Answer 15

K

Question 16

What is the equilibrium position for a non loaded system?

Answer 16

0

Question 17

What is the static equilibrium position characterized by?

Answer 17

All derivatives vanish

Question 18

What is the formula for natural angular frequency \omega_n

Answer 18

\sqrt{k/m}

Question 19

What is formula for daming ratio \cetta

Answer 19

c/(2 \omega_n m)

Question 20

What is formula for damped frequency \omega_d

Answer 20

\omega_n \sqrt{\cetta^2 - 1}

Question 21

What are the three types of damping?

Answer 21

Over/supercritical
Aperiodic/ Critical
Uner/ Subcritical

Question 22

What is sinh(x)?

Answer 22

(e^x - e^-x) / 2

Question 23

What is cosh(x)?

Answer 23

(e^x + e^-x)/2

Question 24

Given same initial conditions, what kind of damping will lead to equilibrium most quickly?

Answer 24

Critical

Question 25

What is the formula for period of damped oscillation?

Answer 25

2\pi / (\omega_d)