Lecture 4 Free Vibration

Question 1

damping is the mechanism by which

Answer 1

energy is dissipated as heat

Question 2

what does damping cause

Answer 2

vibrations to die away

Question 3

Draw a free body diagram of a simple damped system

Answer 3

see book

Question 4

equation of motion of damped system

Answer 4

mx.. + cx. + kx = 0

Question 5

characteristic equation of motion for damped system

Answer 5

ms^2 + cs + k =0

Question 6

critical damping equation

Answer 6

cc = 2 sqart (km) = 2m wn

Question 7

damping ration =

Answer 7

c/cc

Question 8

What does a critically damped system response look like

Answer 8

see book

Question 9

what will a critically damped system do

Answer 9

with have fastest return to equilibrium

Question 10

Over damped system equation

Answer 10

see book

Question 11

damped natural frequency

Answer 11

wc = wn sqrt ( 1 - zeta^2)

Question 12

underdamped system response

Answer 12

see book

Question 13

What equation will an underdamped system osciallate between

Answer 13

e ^ -zetawnt

Question 14

what kind of response is expected for an overdamped system

Answer 14

zeta > 1 sluggish response no oscillation

Question 15

what kind of response is expected for a critically damped system

Answer 15

no oscillations fastest return to equilibrium

Question 16

what kind of response is expected for a underdamped system

Answer 16

oscaillates about equilibrium

harmonic with exponential decay

Question 17

What is the analysis procedure for free vibration systems

Answer 17

free body diagram,
equation of motion
trial solution
roots of char eqn
initial conditions
general solution