### Dynamic Response » Response to Specific Input Functions

The first-order response is characterized uniquely by the time constant 𝜏, so a single representative response to each input function characterizes all such sensors. In the plots that follow, the time constant will be 1 s. However, for a sensor having second-order response, the response is determined by the three terms shown in the equation or as the gain factors in the transfer-function diagram, k, 1/m, and D.

In the transfer function diagram shown, k, D, and 1/m are gain factors affecting the instrument response.

Only the relative sizes of the gain factors are important, so the controlling factors can be reduced to two, the undamped natural angular frequency of the system, given by ω_{0} = √ k/m and the ratio of the damping term to the critical-damping value, given by 𝛄 = D / (2 √ mk ).