Please discuss the nature of bifurcation instability and limit point instability. Discuss the instability problem of perfect and real columns, beams and beam-columns, which type of instability are they?

Ahouse has the following electrical appliance usage (1) single 40w lamp used for 4 hours per day (2) single 60w fan used for 12 hours per day (3) single 200w refrigerator that runs 24 hours per day with compressor run 12 hours and off 12 hours find the solar power inverter size in watt with correction factor of 1.25.

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Aplate clutch has a single pair of mating friction surfaces 250-mm od by 175-mm id. the mean value of the coefficient of friction is 0.30, and the actuating force is 4 kn. a) find the maximum pressure and the torque capacity using the uniform-wear model. b) find the maximum pressure and the torque capacity using the uniform-pressure model.