2. (60%) A multispan, undercritically-damped bridge is loaded with a time-varying force P(t) as shown in Figure 2. Assume rigid body mo- tion of both spans. Note that the mass density of the bridge is different for two spans. Properties of the bridge are: Mass density: m = 2m, Damping: c = c, and T. Yu CIVE.5570 Structural Dynamics 5 Stiffness: k = 2k, k2 = 1.5k. 1 Fall 2023 Derive the dynamic governing equation of motion by using (1) (30%) D'Alembert's Principle, (2) (30%) Lagrange's Equation of Motion. www 3L/2 L/2 L/3 L/3 P(t) - m C www Figure 2: Multispan bridge u(t) HW-01