Free Vibration Flashcards
motions taking place with the applied force set equal to zero
Free vibrations
To establish the free vibration response of the system, there must be no _________ and that the SDOF system is without ________
- ground motion
- damping
The natural frequency f is usually expressed in ____________
hertz or cycles per second
Because the quantity π differs from the natural frequency f only by the constant factor, 2π,
π is also sometimes referred to as the ____________
natural frequency
However, to differentiate, π may be called ___________________ The unit of π is _______
- circular or angular natural frequency
- rad/sec
Amplitude
π=sqrt(π¨^π+π©^π)
The motion is oscillatory with decaying amplitude
Underdamped
The response is similar to the critically damped system, but the return towards neutral position requires more time as the damping ratio is increased
Overdamped
There is no oscillation, and the amplitude decays more rapidly than the former two cases
Critically Damped
The solution changes its form according to the magnitude of the damping factor π
There are 3 cases:
Underdamped, Overdamped, Critically Damped
period T of
π»=ππ /π
natural frequency f
π=π/π»=π/ππ
π =
π¨cosππ+π©sinππ
π (dot) =
βπ¨πsinππ+π©πcosππ
T (natural period) =
ππ xsqrt(π/π)
