Which of the following is correct regarding the principal stresses and maximum in-plane shear stresses? a. principal stresses cannot be negative. b. the shear stress over principal stress planes is always zero. c. a principal stress plane can be reached by rotating the maximum in-plane shear stress plane 90° in the clockwise direction. d. the maximum in-plane shear stress is always smaller than principal stresses.

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.