The three-dimensional motion of a particle is defined by the position vector: ~r = (Rt cosω n t) ~i + ct~j + (Rt sinω n t) ~k. Determine the magnitudes of the velocity and acceleration of the particle. show that the space curve described by the particle is a conic helix.

Amass of 1.5 kg of air at 120 kpa and 24°c is contained in a gas-tight, frictionless piston-cylinder device. the air is now compressed to a final pressure of 720 kpa. during the process, heat is transferred from the air such that the temperature inside the cylinder remains constant. calculate the boundary work input during this process.

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.

Items are similar to the free issue items, but their access is limited. (clo5) a)-bin stock items free issue b)-bin stock controlled issue c)-critical or insurance spares d)-rebuildable spares e)-consumables