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Amass-spring-viscous damper system of mass 3 kg has a frequency of 100 rad/s and is critically damped. its initial conditions are x(0)-3 mm and (0)-2.3 m/s. does the system overshoot its equilibrium position? prove your answer

Air at a pressure of 1atm and a temperature of 40 c is in parallel flow over the top surface of a flat plate that is heated to a uniform temperature of 120 c. the plate has a length of 0.40m (in the flow direction) and a width of 0.15m. the reynolds number based on the plate length is 50, 000. what is the rate of heat transfer from the plate to the air? if the free stream velocity of the air is doubled and the pressure is increased to 10 atm what is the rate of heat transfer?

Consider a power plant with water as the working fluid that operates on an ideal rankine cycle. it has a net power output of 45mw. superheated steam enters the turbine at 7mpa and 500°c (h=3411.4 kj/kg; s=6.8 kj/kg k) and is cooled in the condenser at a pressure of 10 kpa by running cooling water from a lake through the tubes of the condenser at a rate of 2000 kg/s. (a) show the cycle on a t-s diagram (a right schematic is fine - you do not need to calculate the temperatures at each point); (b)-determine the work done by the turbine and the pump in kj/kg; (c)-the mass flow rate of water used by the power plant; (d)-the thermal efficiency of the cycle; (e)-the temperature rise of the cooling water. assume the cooling water is incompressible with cp 4.18 kj/kg°c.