Analyze the cube provided in the figure below. Positive directions in the coordinates system of base vector (i⃗ , j⃗ , k⃗ ) are defined as show by the arrowheads and the right-hand.

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.

Refrigerant 134a enters an insulated compressor operating at steady state as saturated vapor at -26°c with a volumetric flow rate of 0.18 m3/s. refrigerant exits at 9 bar, 70°c. changes in kinetic and potential energy from inlet to exit can be ignored. determine the volumetric flow rate at the exit, in m3/s, and the compressor power, in kw.

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.