Problem on degree of freedom

Draw a frequency-response curves for a damped single degree of freedom system subjected to a harmonic excitation under three different damping ratios. System has a natural frequency of ω_n as the forcing frequency of the excitation is ω. Describe 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 define whether the dynamic response is controlled by the mass, or stiffness or damping of the system for each and every case.

(b) The single degree of freedom building system is excited by a sinusoidal force as shown in figure below. 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 10⁶ mm⁴ and 5 % damping and neglect the mass of columns. Find out

(i) the steady state amplitude of vibration,
(ii) the maximum shear force in the column,
(iii) the maximum bending moment.

973_degree of freedom.jpg

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