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Consider (Figure a) a single-story building is a single-degree-of-freedom system, the column provides massless lateral stiffness k, and the rigid version has a total mass m. Imagine that an earthquake is an acceleration pulse, and its acceleration duration can be expressed as g(1) gos(1) no damping. Please derive the displacement spectrum (Sd), velocity spectrum (PSV), acceleration spectrum (PSa) mathematical formulas and plots (horizontal axis T). . Explain that under this earthquake, is there any difference between the real velocity spectrum (Sv) and the real acceleration spectrum (Sa) and PSV and PSa? If there is damping, please prove the maximum displacement response formula. go Umax = exp 0 ( sin-'1- Ground velocity Time, Totul suffness Ground accelnation Ugo8(t) 77777 Time, (a) Consider (Figure a) a single-story building is a single-degree-of-freedom system, the column provides massless lateral stiffness k, and the rigid version has a total mass m. Imagine that an earthquake is an acceleration pulse, and its acceleration duration can be expressed as g(1) gos(1) no damping. Please derive the displacement spectrum (Sd), velocity spectrum (PSV), acceleration spectrum (PSa) mathematical formulas and plots (horizontal axis T). . Explain that under this earthquake, is there any difference between the real velocity spectrum (Sv) and the real acceleration spectrum (Sa) and PSV and PSa? If there is damping, please prove the maximum displacement response formula. go Umax = exp 0 ( sin-'1- Ground velocity Time, Totul suffness Ground accelnation Ugo8(t) 77777 Time, (a)