Simple level in a tank system has $10cm$ diameter and height of $50cm.$ Initially system was at steady state where height of the liquid was measured as $30cm$ and corresponding liquid flow was $3L\frac{t}{m}in.$ Two minutes after the steady state was reached inlet flow rate was increased to $4\frac{L}{m}in$ and maintained for a period of $3$min, then the flow rate was reduced to $2L\frac{t}{m}in.$ there after. Represent the imput sequence Graphically as well as in time and Laplace domains. Draw the plot between height of liquid in the tank against time in minutes with a sampling time of $1$ min starting from the initial steady state.

OR

Simple thermometer having time constant of $6$Sec was at ambient temperature of $30C.$ It was immersed into water bath having temperature of $50C$ and kept there for a period of $0\mathrm{.}1$min. Then it was transferred to a constant temperature water bath maintained at $30C$ for a period of $0\mathrm{.}2$min before it is shifted in to cold water at $10C.$ Represent the input sequence Graphically as well as in time and Laplace domains.

Draw the plot between temperature shown by themometer against time with a sampling time of $3sec$ starting from initial steady state for a period of $24sec.$