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1. Two carts with negligible rolling friction are connected as shown in Figure 1. An input force u(t) is applied. The masses of the two carts are M₁ and M2 and their displacements are denoted as x(t)) and q(t), respectively. The two carts are connected by springs, k₁, k2 and dampers b₁, b₂. x(t) g(t) k₁ k, M₁ M, u(t) Figure 1 By using Newton's Second Law, derive the two equations that describe the motion of the two carts. Hence derive the transfer function that relates the displacement q(t) and the input u(t), i.e. G(s) : = Q(s) U(s) Support your answer with complete working steps and explanation.

1. Two carts with negligible rolling friction are connected as shown in Figure 1. An input force u(t) is applied. The masses of the two carts are M₁ and M2 and their displacements are denoted as x(t)) and q(t), respectively. The two carts are connected by springs, k₁, k2 and dampers b₁, b₂. x(t) g(t) k₁ k, M₁ M, u(t) Figure 1 By using Newton's Second Law, derive the two equations that describe the motion of the two carts. Hence derive the transfer function that relates the displacement q(t) and the input u(t), i.e. G(s) : = Q(s) U(s) Support your answer with complete working steps and explanation.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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1. Two carts with negligible rolling friction are connected as shown in Figure 1. An input force u(t) is applied. The masses of the two carts are M₁ and M2 and their displacements are denoted as x(t)) and q(t), respectively. The two carts are connected by springs, k₁, k2 and dampers b₁, b₂. x(t) g(t) k₁ k, M₁ M, u(t) Figure 1 By using Newton's Second Law, derive the two equations that describe the motion of the two carts. Hence derive the transfer function that relates the displacement q(t) and the input u(t), i.e. G(s) : = Q(s) U(s) Support your answer with complete working steps and explanation.
Transcribed Image Text:1. Two carts with negligible rolling friction are connected as shown in Figure 1. An input force u(t) is applied. The masses of the two carts are M₁ and M2 and their displacements are denoted as x(t)) and q(t), respectively. The two carts are connected by springs, k₁, k2 and dampers b₁, b₂. x(t) g(t) k₁ k, M₁ M, u(t) Figure 1 By using Newton's Second Law, derive the two equations that describe the motion of the two carts. Hence derive the transfer function that relates the displacement q(t) and the input u(t), i.e. G(s) : = Q(s) U(s) Support your answer with complete working steps and explanation.
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