Lecture 4 Free Vibration Flashcards
damping is the mechanism by which
energy is dissipated as heat
what does damping cause
vibrations to die away
Draw a free body diagram of a simple damped system
see book
equation of motion of damped system
mx.. + cx. + kx = 0
characteristic equation of motion for damped system
ms^2 + cs + k =0
critical damping equation
cc = 2 sqart (km) = 2m wn
damping ration =
c/cc
What does a critically damped system response look like
see book
what will a critically damped system do
with have fastest return to equilibrium
Over damped system equation
see book
damped natural frequency
wc = wn sqrt ( 1 - zeta^2)
underdamped system response
see book
What equation will an underdamped system osciallate between
e ^ -zetawnt
what kind of response is expected for an overdamped system
zeta > 1 sluggish response no oscillation
what kind of response is expected for a critically damped system
no oscillations fastest return to equilibrium
what kind of response is expected for a underdamped system
oscaillates about equilibrium
harmonic with exponential decay
What is the analysis procedure for free vibration systems
free body diagram, equation of motion trial solution roots of char eqn initial conditions general solution
