If the coordinate axes are principal axes, so that the stress matrix has the form

[ 1 0 0

0 2 0

0 0 3 ]

(a) Determine the normal component and the magnitude of the tangential components of the traction vector on a plane with unit normal = x + y + z.

(b) Determine also the components of a unit vector in the plane, such that = + .

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.

Which of the following controllers anticipates the future from the slope of errors over time? a)-proportional b)-on/off c)-integral d)-derivative.

How much power could a wind turbine produce if it had the following specifications? cp = 0.45 -d=1.2kg/m3 d=50m v 5m/s