The response of the deflection of a fluid-filled catheter to changes in pressure can be modeled using a second-order model. Knowledge of the parameters of the model is important because in cardiovascular applications the undamped natural frequency should be close to five times the heart rate. However, due to sterility and other considerations, measurement of the parameters is difficult. A method to obtain transfer functions using measurements of the amplitudes of two consecutive peaks of the response and their timing has been developed (Glantz, 1979). Assume that Figure P4.13 is obtained from catheter measurements. Using the information shown and assuming a second-order model excited by a unit step input, find the corresponding transfer function.

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Step Response 1.6 1.4 sysem: T Time (sec o.nsns Amplitude: 1.15 1.2 iSystem: T Time (secjk 00674 Ampitude: 0.923 0.8 0.6 0.4 0.2 0.05 0.1 0.15 Time (sec) FIGURE P4.13 Amplituce