Q$3/$ A temperature control loop has been designed for a a particular process. The loop have $\frac{1}{6}$ decay ratio and for there to be no offset between the set point and measure value of the temperature. To test the loop, operators provided a disturbance to a system by instananteously changing the flow stream by $3$ degree higher than the set point temperature. The period of oscillation was $10$min. Determine:

The second order transfer function for the process.

The maximum temperature that observed.

When the maximum temperature occurred.