A high rise tower like Burj Khalifa can be considered as a single degree of freedom system under transverse vibrations. The logarithmic decrement of the newly buils structure is 5.0 and the natural frequency is 0.2 Hz. A wind gust induces a velocity of 0.3 m/s to the structure while the building is at rest in the equilibrium position. (1) Find out the free vibration response of the newly built structure. (i) What is the displacement of the newly built structure after Isecond? (iii) Now, cracks develop inside the structure over a period of time and due to which the stiffness of the aged structure reduces by 40% and the damping coefficient increases by 50%. Find out the free vibration response of the aged structure with cracks with same initial condition due to wind. (iv) What is the displacement of the aged structure (with cracks) after I second.