Draw the zeta=0.707 line. then the intersection point btwn the RL and zeta line in the location of the cl complex pole. Derive the characteristic eq, then replace s by the cl pole to get K. K should be real and +. or use K=-(denominator)/(numerator) of G(s).
wn can be found from the complex cl pole using the pythagorian.

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.