Find the continuous-time Fourier series (CTFS) coefficients ak. Simplify the expression as much as possible. You might want to use the fact that e^−jπ = -1, e^-jπ/2 = -j, e^-j3π/2 = j, and e^-j2π =1. Also, taking the expression into e-jkπ/4 parenthesis will help.

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.