The total vertical force, Q, exerted on the base of a mat is 2,000,000 lbs. The mat is 25 feet by 50 feet with an embedment depth of 3 feet in soil having a unit weight of 120 pcf. The gross ultimate bearing capacity for the mat was determined to be 5,000 psf. What is the factor of safety against a bearing capacity failure based on the net ultimate bearing capacity?

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.