1. (a) Sketch frequency-response curves for a damped single degree of freedom system subjected to a harmonic excitation under three different damping ratios. The system has a natural frequency of ω_{n} while the forcing frequency of the excitation is ω. Explain the relation of static and dynamic deformation responses for
(i) ω/ω_{n} << 1
(ii) ω/ω_{n} >> 1
(iii) ω/ω_{n} = 1
Also state whether the dynamic response is controlled by the mass, stiffness or damping of the system for each case.
(b) A single degree of freedom building system is excited by a sinusoidal force as shown in Figure 1. Assume that the girder is rigid whereas the columns are flexible to the lateral deformation but rigid in the vertical direction. Use E = 30 GPa, I = 60 x 10^{6} mm^{4} and 5 % damping and neglect the mass of columns. Determine
(i) The steady state amplitude of vibration,
(ii) The maximum shear force in the column,
(iii) The maximum bending moment.