Figure Q2 shows an impulsive acceleration having duration 0.02 seconds and maximum magnitude of 10 m/sec. 10 accn. [m/sec] 0.2 0.4 0.6 0.8 1 time [seconds] Figure Q2 a) If a single degree of freedom vertical structure (like a water tower) with natural frequency of 2 Hz and very small damping experiences the ground motion shown in Figure Q2 with no subsequent shaking, calculate the absolute displacement response of the ground and the mass of SDOF structure and plot them on a same graph for the first 1 second. b) For zero damping, plot the acceleration response spectrum for the above earthquake. Use period for the horizontal axis from zero to 10 seconds. A two-storey building that responds to the ground motion shown in Figure Q2 is represented as an undamped two degree of freedom 'stick model' having mass and stiffness matrices: 500000 M = 0 0 500000 kg K = 200 -200 -200 700 MN/m The mode shapes and modal frequencies are calculated as: [1.000 -0.351] [] = 0.351 1.000 {2}={16.115 39.247} c) determine for both modes, the modal mass mr, the earthquake excitation factor Lr, and the effective mass L Mr d) Sketch base shears for both modes during the first second of response and determine the absolute maximum total value during this period. e) Use your response spectrum from part (b) to estimate the peak base shear and comment on any difference in the values.