At resonance the amount of energy lost due to damping is equal to the rate of energy supply from the driver. The driver is the source of external energy that keeps the oscillations going — for example, the person pushing a kid on a swing. Increasing the damping will reduce the size amplitude of the oscillations at resonance, but the amount of damping has next to no effect at all on the frequency of resonance.
Damping also has an effect on the sharpness of a resonance. Sharp jagged waveforms will be produced. Conversely, an over-damped system will produce underestimated values and slurred broad waveforms. With overdamping, some of the higher frequency harmonic waveforms will be lost remember that these are the waveforms which already have a lower amplitude; with more damping their amplitude disappears to near zero. The changes in waveform shape can be illustrated in a situation where the damping coefficient of a system is gradually increased while oscillations are occurring - in this case, a dog's pulse.
Because damping increases dramatically with decreasing tube diameter, one may conveniently model an increasing damping coefficient by tightening a clamp over the arterial line tubing, just as Geddes et al did in Note how first, the dicrotic notch is lost because it is produced by high frequency, low amplitude elements. Then, the waveform begins to flatten as the amplitude of even the low-frequency waves is affected.
At last, with the tubing clamped, the waveform flattens at the mean arterial pressure. The frequency response of a system is the relationship between the frequency of the measured waves and the amount of amplitude amplification which might occur as the result of resonance. From this, the beneficial effects of damping become clear. The damped system has a larger range over which there is little amplitude increase with increasing frequency, and even at its natural frequency the amplitude change is smaller.
As a result, the measured pressure waves will not be overestimated as much. In an ideal system, all frequencies of clinical interest will lie within this flat range.
For an arterial line, for example, that would be all eight harmonics - i. So, how do you know what the frequency response of a system is? For arterial line pressure transducers, the "fast flush test" is the clinical bedside test which is used to assess the natural frequency of the system.
To return to the model of the transducer system as a simple harmonic oscillator, this "fast flush" is dropping the ball from a height, or giving the pendulum a gentle nudge. Then you watch it and wait for it to swing through a few oscillations, and measure the frequency. In effect that is what you're doing when you open the fast flush valve on the arterial line transducer set. The "bounce" of oscillations after a fast flush can be recorded on graph paper, vellum parchment or wet clay if you have a dislike of computers.
More likely, as an intensivist you're an intensely technophilic organism, and prefer to measure the time interval between oscillations with the convenient digital calipers integrated into most monitoring software packages.
You'd get a number, typically in milliseconds. That can be converted to a frequency in Hz the number of oscillations per second.
This is the natural frequency of your transducer system. If the natural frequency is over Hz, you'd be able to confidently say that the clinically relevant range of frequencies Hz is well within the flat range of this system, and the pressure values you are recording are accurate.
Generally speaking, at the bedside you will find most arterial line systems have a natural frequency somewhere between 10 and 25 Hz Schwid et al, Moxham, I.
Stoker, Mark R. Gilbert, Michael. Schwid, Howard A. Gardner, Reed M. Resonance, damping and frequency response. Previous chapter: Pressure transducers for haemodynamic measurements Next chapter: Physiological basis of electrocardiography. A graph of position vs. Figure 8. The effect on the energy of the system is obvious — the non-conservative drag force converts mechanical energy in the system into thermal energy, which is manifested as ever-decreasing amplitude recall the simple relationship total energy has to amplitude, shown in Equation 8.
It should not be surprising therefore what we find in the next case In this case, the sinusoidal behavior goes away. This kind of motion is called critically-damped. The easiest way to get a handle on this is to simply plug the condition into the solution, Equation 8. We see that the oscillatory motion is gone the sine function just includes the phase constant, so there is no time dependence in the sine function. This is strange case is called overdamped. The effect of damping on resonance graph: The amplitude of the resonance peak decreases and the peak occurs at a lower frequency.
So damping lowers the natural frequency of an object and also decreases the magnitude of the amplitude of the wave. Phase and resonance: The phase relationship between the driving oscillation and the oscillation of the object being driven is different at different frequencies. From Wikibooks, open books for an open world.
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