Using the “TransferFunction” Shiny App -- pls wait for the plot to appear above

The plots show the assumed input as a red line. The calculated response uses, for first-order response, a simple exponential with time constant τ = 1. This response in each case is displayed as the blue line described as “M1” in the legends. If the "1st-order damping" checkbox is selected, damping is applied having magnitude controlled by the "log gamma" slider, which can vary the damping from none to enough to eliminate any response at the two limits of the slider. (This is equivalent to changing the time constant of a first-order system.) For second-order response for the system displayed, which is a damped harmonic oscillator, the resulting lines are labeled “M2” and plotted as green lines. This second-order sensor is characterized by two parameters, taken to be omega (ω) and gamma γ, and they can be controlled by two sliders in the sidebar panel. The natural undamped oscillation angular frequency is specified by ω and the ratio of the amount of damping to the critical amount is specified by γ, so that γ = 1 specifies critical damping and smaller values can oscillate and overshoot while larger values respond slowly. The slider controlling the frequency applies only to repetitive waveforms like the sine or square waves. All these sliders are set using base-10 logarithms to provide a better range than is possible with a linear slider, and the values actually used are then included in the titles of the plots. The "More Info" button will cause another browser window to open with additional information.