Find the mass and center of mass of the lamina that occupies the region d and has the given density function rho. D is bounded by y = 1 − x2 and y = 0; rho(x, y) = 7ky.

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.

Water at the rate of 1 kg/s is forced through a tube with a 2.5 cm inner diameter. the inlet water temperature is 15°c, and the outlet water temperature is 50°c. the tube wall temperature is 14°c higher than the local water temperature all along the length of the tube. what is the length of the tube?

Find the minimum film thickness for a journal bearing with the data below. shaft diameter, d-50 mm, clearance ratio, cdratio? 0.001, shaft speed, n 2000 rpm; bearing length. i 200 mm; eccentricity ration, ? -0.55. ( note, cdratio-ca/d) the minimum film thickness is um