Obtain the natural frequencies and mode shapes for a free-free uniform beam in lateral vibration and plot the first three modes. ignore the rigid-body modes

Steam enters a converging nozzle at 3.0 mpa and 500°c with a at 1.8 mpa. for a nozzle exit area of 32 cm2, determine the exit velocity, mass flow rate, and exit mach number if the nozzle: negligible velocity, and it exits (a) is isentropic (b) has an efficiency of 94 percent

Estimate the change in specific internal energy au and specific enthalpy h from inlet to outlet for ethylene glycol (a liquid) flowing through each of the following devices: (a) a heat exchanger where the glycol temperature increases from 20 °c to 80 °c; (b) a pump operating at about 25 °c and increasing the glycol pressure from 100 kpa to 8 mpa.

Air (c-1.006 kj/kg. k, r-0.287 kj/kg. k) enters a nozzle steadily at 280 kpa and 77°c with a velocity of 50 m/s and exits at 85 kpa and 320 m/s. the heat losses from the nozzle to the surrounding medium at 20°c are estimated to be 3.2 kj/kg. determine (a) the exit temperature and (b) the total entropy change for this process. solve this problem using constant specific heats.