Hi looking for some help on the below I'm a little bit stuck. The effect of an earthquake on an elevated water tank is to be investigated. The water tank has mass m=2x10^6 kg and natural frequency wn=10.6 rad/s and a damping coefficient of 12% critical damping. Ground acceleration can be approximated by constant spectrum So=0.0075m2/s3 Obtain: i) The frequency response function for the displacement of tank mass relative to the ground ii) Mean square response of displacement iii) Standard deviation of displacement Frequency Response = Output / Input mz"+cz'+kz=-my" ........................................Eq 1 Where z is the relative displacement and y is input I've done some work on something similar in the past where I have used the Force input to the system to get the frequency response function and obtain the equation: H(w) = 1 / (k-(mw^2)+icw This gives the frequency response function of the elevated mass displacement relative to the input force? Using the equation: mz"+cz'+kz=-my" If I take the input displacement y = Ae^iwt (where A is a constant then) y' = iwtAe^iwt y"= -w^2.Ae^iwt The output would then be z = Be^iwt z' = iwtBe^iwt z" = -w^2.Be^iwt subtituting into Eq 1 (k+iwc-mw^2)B.e^iwt = (mw^2)A.e^iwt Therefore response is equal to B/A = (mw^2) / (k+iwc-mw^2) Is this along the correct lines??