This program illustrates the response of a damped pendulum seismometer to various driving functions and output filtering. The period of the pendulum is equal to five major divisions on the display screens (100 pixels). The plot width is equal to 6 pendulum periods (600 pixels).
The top screen displays the input ground velocity.
The middle screen displays the resulting response of the seismometer.
The bottom screen displays the output after application of various filters to the raw response given in the middle screen. No filters have been implemented for the displacement mode of display.
There are three types of driving functions, (1), sinusoidal of controllable period, (2), a velocity impulse, and (3) a displacement of the pendulum from equilibrium as the initial condition.
The pendulum damping is controlled by the value selected for Q. For those who use damping factor as a descriptor, it is equivalent to 0.5/Q. A Q of 0.5 corresponds to a damping factor of 1.0, which is critical damping.
There are 9 command buttons on the display. Three of them cause dialog boxes to open up for user input. These are "Q", "Pin/Pp", and "Filter". The driving frequency is specified by specifying a value for Pin/Pp, which is the ratio of the period of the driving frequency divided by the period of the pendulum. The filter button allows the user to select one of several options. A description of the remaining buttons follows:
"Run" initiates a sinusoidal drive waveform whose period is controlled by Pin/Pp.
"Continue" allows continued plotting on a refreshed plotting surface of a run.
"Stop" will terminate a run. It is really superflous, as execution is suspended automatically at the time limit of the plotting surface.
"Tap" provides a velocity impulse, independent of the value set up for Pin/Pp.
"Drop" starts a run in which the initial condition is a displacement of the pendulum from equilibrium, followed by a release.
"Clear Screen" erases the plotting screens, which are otherwise only erased by clicking "Continue". By not using "Clear Screen after a run, additional runs can be superimposed on the plotting screens. This allows plotting of a family of curves in which only one parameter is varied, such as "Q" ,filter period, or Pin/Pp.
Additional control of Pin/Pp is provided by mouse clicks on the top display screen. Clicking with the left mouse button will double the current value of Pin/Pp and initiates a run at the new period. Clicking with the right mouse button halves the current value of Pin/Pp and initiates a run a the new value.
Note that the seismometer, when driven at its natural frequency, has a response which is leading in phase by 90 degrees, and whose amplitude is proportional to Q.
Filter number 2 implements my own design. If you experiment with it, you will find that it can not only extend the period response to far longer period than the natural period of the pendulum, but it can also compensate for having the damping too low or too high. Note that it can largely remove the ringing that occurs when the pendulum is underdamped. Try setting seimometer Q to 1.8, and examining the tap test response with and without the filter. I use it for extending the useful response of my own seismometers to periods of 30 seconds or more, even though the sensors have much shorter natural periods.