A linear, time-invariant, causal continuous-time system has a rational transfer function with simple poles at s = -2 and s = -4, and one simple zero at s = -1. A unit step u(t) is applied at the input of the system. At steady state, the output has a constant value of 1. The impulse response of this system is:

Asolid cylinder is concentric with a straight pipe. the cylinder is 0.5 m long and has an outside diameter of 8 cm. the pipe has an inside diameter of 8.5 cm. the annulus between the cylinder ad the pipe contains stationary oil. the oil has a specific gravity of 0.92 and a kinematic viscosity of 5.57 x 10-4 m2/s. most nearly, what is the force needed to move the cylinder along the pipe at a constant velocity of 1 m/s?

Ahe-xe mixture containing a 0.75 mole fraction of helium is used for cooling electronics in an avionics application. at a temperature of 300 k and atmospheric pressure, calculate the mass fraction of helium and the mass density, molar concentration and molecular weight of the mixture. if the cooling capacity is 10 l, what is the mass of the coolant?

A2-m rigid tank initially contains saturated water vapor at 100 kpa. the tank is connected to a supply line through a valve. steam is flowing in the supply line at 600 kpa and 300 c. the valve is opened, and steam is allowed to enter the tank until the pressure in the tank reaches the line pressure, at which point the valve is closed. a thermometer placed in the tank indicates that the temperature at the final state is 200°c. determine (a) the mass of steam that has entered the tank (b) the amount of heat transfer.