This document discusses the dynamic characteristics of transducers. It includes questions about sketching the response of first and second order systems to step inputs and writing the governing equations. It also includes a question about calculating the time constant of a medical thermometer that is modeled as a first order system based on temperature measurements taken over time.

1. Measurements and Instrumentation Instructor: Dr. Mohamed Rashed
ME305
Fall 2021
Sheet 3
Transducer Dynamic Characteristics
1. Sketch the dynamic response of a first -order system to a step input. Show the time
constant on the sketch. Also write the differential and algebraic equations governing this
system.
2. Plot the non-dimensional output signal versus the time constant of a first order dynamic
system for a step input. Then, plot the dynamic response of a sensor with a larger time
constant.
3. Sketch the dynamic response of a second order system to a step input for different damping
ratios. Also write the differential equation governing this system.
4. A medical thermometer is administered to a patient. The initial thermometer temperature
was the local room temperature (22°C). After 10 s the indicated temperature reached
28.5°C. After a very long time, the thermometer reached a steady state indicating 38.5°C.
a) Assuming that the thermometer behaves as a first order system, calculate its time
constant.
b) Due to budget cuts in the hospital, it is important to make the temperature
measurements as quickly as possible. Find out the time it takes for the thermometer
to approach the steady-state temperature to within 0.1°C.