ME 365 HOMEWORK SET 5 Spring 2010 Out: Thursday, February 11 2010 Due: Thursday, February 18 2010 -1- Solve each problem on separate sets of sheets. Dynamic System Response—Time Response Problem 1 (First Order Step Response) The time response of a thermocouple is described by the following first order differential equation: 0dy y KT V dt where y is the output voltage, T is the input temperature, is the time constant, K is the static sensitivity, and V0 is the bias voltage. For an initial temperature T0 , a final temperature of T f , with a step change in external temperature T at time t=0 and initial voltage output y(0)=KT0 , find the following: a. The particular solution of the differential equation or the steady state response of the thermocouple. b. The homogeneous solution of the differential equation or the transient response of the thermocouple. c. Determine the overall time response of the thermocouple. d.
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