How to calculate moment of inertia of a cracked transformed cross-section.

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.

The thermal expansion or contraction of a given metal is a function of the f a)-density b)-initial temperature c)- temperature difference d)- linear coefficient of thermal expansion e)- final temperature f)- original length

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