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Normally we only consider the effects of a driving force on a damped, harmonic oscillator. Briefly...

Normally we only consider the effects of a driving force on a damped, harmonic oscillator. Briefly describe two problems, or significant differences, we would encounter if we tried to consider the effect of a driving force on an undamped oscillator.

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Answer #1

Normally we just consider effects of driving force on damped oscillator
For example, effect of as push/pull on a damped door closer etc.
Driving force on undamped oscillator
the equation of motion can be written as
mx" + kx = Focos(wt + phi*)
the solutoin has a general form
x(t) = xtansient + xsteady
xtransient = A'*e^(-gamma*t)sin(w't + phi')
here, 0
A' = (xo - Acos(phi))/sin(phi')
phi = - phi*
w' = wo = sqroot(k/m)
and
phi' = arctan[wo(xo - Acos(phi*))/(vo + Awsin(phi*))]

tranisent solution has a frequency of wo ( the natural frequency of the system)

xsteady = Acos(wt + phi*) -> Totally determined by the driving force
so the osscilation is always in phase with the dricing case in undamped osscilator which is noit the case in damped osscilator where there comes a phase difference in osscilation and force bec ause of damping

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