Consider this three-story parking garage. (K, 2-10% b = 2.104 Sec VO/ neek 23.10/ces (b =...

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Consider this three-story parking garage. (K, 2-10% b₁ = 2.104 Sec VO/ neek 23.10°/ces² (b₂ = 3-10² My love, (K₂ = 367 • 10² 40/² (6₂ = 2.2.10² ky love) 7777 m, 48000 un 3₂.9000 k my = 11 000 ky M₂ ₁+ A₁ (₁) M₂ ₂+k₁ (2₁) + ₂(x₂-x₂) My By+k₂ (₁2₂) + A₂ (2-3) 7 grand We are going to model the horizontal motion of each level of the parking garage to due to a simulated "earthquake". i.e. by assuming that at time to the ground shifts suddenly to the right: (b) Then set up the problem in matrix-vector form 47 t-0. y(t)-y-0.3m) (a) Using your preferred derivation method and neglecting damping, confirm that the three coupled equations of motion of levels r(t). (t). and (), are 0 X₂ (t) 1. [M] Max[M], with Mate 10kg), and ii. [K] Kalex [K],with Kscale=10(kg/mc). [8001 pyle) 0 (0) 0 0.2₂(0) 0 0; 23(0)-0; 7(0)-74(0)-7 kapo with 7-[], with [M] the dimensioned "maas" matrix, and [K] the dimensioned "stiffness" matrix. +=Kscale/Micale! Furthermore, because the only length scale in this problem is po, let: 7-7/90- (c) Each of the dimensioned matrices above can be written as a "typical dimensioned scale" times a pure-number matrix, viz For example: [M] Max 090-Micale [M], with M10(kg) 0 0 11 (d) The form of the equation suggests that the dimensionless timescale should be So show that the system, pond in dimensionless and r variables, is M+K17-0 dr² "Three-level panking garage (0) 0: (0) 0 (0) - 0; 47-(-9). 7(0)-6;4(0)-0: Consider this three-story parking garage. (K, 2-10% b₁ = 2.104 Sec VO/ neek 23.10°/ces² (b₂ = 3-10² My love, (K₂ = 367 • 10² 40/² (6₂ = 2.2.10² ky love) 7777 m, 48000 un 3₂.9000 k my = 11 000 ky M₂ ₁+ A₁ (₁) M₂ ₂+k₁ (2₁) + ₂(x₂-x₂) My By+k₂ (₁2₂) + A₂ (2-3) 7 grand We are going to model the horizontal motion of each level of the parking garage to due to a simulated "earthquake". i.e. by assuming that at time to the ground shifts suddenly to the right: (b) Then set up the problem in matrix-vector form 47 t-0. y(t)-y-0.3m) (a) Using your preferred derivation method and neglecting damping, confirm that the three coupled equations of motion of levels r(t). (t). and (), are 0 X₂ (t) 1. [M] Max[M], with Mate 10kg), and ii. [K] Kalex [K],with Kscale=10(kg/mc). [8001 pyle) 0 (0) 0 0.2₂(0) 0 0; 23(0)-0; 7(0)-74(0)-7 kapo with 7-[], with [M] the dimensioned "maas" matrix, and [K] the dimensioned "stiffness" matrix. +=Kscale/Micale! Furthermore, because the only length scale in this problem is po, let: 7-7/90- (c) Each of the dimensioned matrices above can be written as a "typical dimensioned scale" times a pure-number matrix, viz For example: [M] Max 090-Micale [M], with M10(kg) 0 0 11 (d) The form of the equation suggests that the dimensionless timescale should be So show that the system, pond in dimensionless and r variables, is M+K17-0 dr² "Three-level panking garage (0) 0: (0) 0 (0) - 0; 47-(-9). 7(0)-6;4(0)-0:

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