Derive from first principles the expression for the response of the tank level (as a deviation from nominal operating conditions) assuming that the input is a perfect sinusoid with the given amplitude but a yet unspecified frequency, . For a given frequency of 0.2rad/h, plot on the same graph the periodic input loading function and the tank-level response. Compare these two functions. (b) (3 points) In terms of the frequency of the periodic loading, what is the maximum deviation from nominal tank level that will be observed? (c) (3 points) Given now that the tank is 10ft high, and that the nominal operating level is 5ft, what condition must the loading frequency satisfy to guarantee that during any particular shift, the tank neither overflows nor runs dry? Derive from first principles the expression for the response of the tank level (as a deviation from nominal operating conditions) assuming that the input is a perfect sinusoid with the given amplitude but a yet unspecified frequency, . For a given frequency of 0.2rad/h, plot on the same graph the periodic input loading function and the tank-level response. Compare these two functions. (b) (3 points) In terms of the frequency of the periodic loading, what is the maximum deviation from nominal tank level that will be observed? (c) (3 points) Given now that the tank is 10ft high, and that the nominal operating level is 5ft, what condition must the loading frequency satisfy to guarantee that during any particular shift, the tank neither overflows nor runs dry