I need help finding the coordinate centroid

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.

Thermal stresses are developed in a metal when its a) initial temperature is changed b) final temperature is changed c) density is changed d) thermal deformation is prevented e) expansion is prevented f) contraction is prevented

Steam enters a converging nozzle at 3.0 mpa and 500°c with a at 1.8 mpa. for a nozzle exit area of 32 cm2, determine the exit velocity, mass flow rate, and exit mach number if the nozzle: negligible velocity, and it exits (a) is isentropic (b) has an efficiency of 94 percent