Find the transfer function of the following system. Find the range of R such that the system C(s)/R(s) is stable, marginally stable, and unstable. Present detailed hand computation/derivation in the report.

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.

Aflywheel accelerates for 5 seconds at 2 rad/s2 from a speed of 20 rpm. determine the total number of revolutions of the flywheel during the period of its acceleration. a.5.65 b.8.43 c. 723 d.6.86

Machinery that is a key part of the process and without which the plant or process cannot function is classifed as: (clo4) a)-critical machinery b)-essential machinery c)-general purpose machinery d)-none of the specified options.