A building has two rooms, only one of which is heated. The first room has a heating system that allows the temperature T1 to be set. (Assume that the response of the heater is instantaneous, so that T1 is always at the desired temperature). In order to condition the other room, air is blown from room 1 to 2, with a seperate return back to room 1. You are tasked with determining the air flow such that the second room will equilabrate within 15 minutes. The system transfer function is given by T, (s) 0.1m T2(s) + 0.1m
a. Suppose at time t = 0, T1 goes from 0 to 1. T1 is a unit step function, Find T2(t). Solution will be a function of \dot{m} PLEASE SHOW WORK & EXPLAIN IF POSSIBLE.
b. Find \dot{m} such that T2(900) = 0.99. That is, T2 reaches 99% of T1 within 15 minutes. PLEASE SHOW WORK & EXPLAIN IF POSSIBLE.