Question: The dynamic behavior of a pressure sensor / transmitter can be expressed as a first-order transfer function (in deviation variables) that relates the measured value

The dynamic behavior of a pressure sensor / transmitter can be expressed as a first-order transfer function (in deviation variables) that relates the measured value P_m to the actual pressure, P:

P′_m(s) / P′(s) = 1 / 30s + 1

Both P_m and P have units of psi and the time constant has units of seconds. Suppose that an alarm will sound if P_mexceeds 45 psi. If the process is initially at steady state (P̅_m = P̅ = 35 psi), and then P suddenly changes from 35 to 50 psi at 1:30 PM, at what time will the alarm sound?

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