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Two carts with negligible rolling friction are connected as shown in Figure (1b). An input force u(t) is applied. The masses of the two carts are M, and M, and their displacements are x(1) and q(t), respectively. The carts are connected by a spring k and a damper b. Answer the following questions: (b) By using Newton's Second Law, derive two mathematical equations that describe the motion of the two carts. Hence derive the following two transfer functions: G,(s) = Q(s) U(s) (c) x(1) q(1) k M, u(t) Figure (1b)

Two carts with negligible rolling friction are connected as shown in Figure (1b). An input force u(t) is applied. The masses of the two carts are M, and M, and their displacements are x(1) and q(t), respectively. The carts are connected by a spring k and a damper b. Answer the following questions: (b) By using Newton's Second Law, derive two mathematical equations that describe the motion of the two carts. Hence derive the following two transfer functions: G,(s) = Q(s) U(s) (c) x(1) q(1) k M, u(t) Figure (1b)

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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Solve part c only

Two carts with negligible rolling friction are connected as shown in Figure (1b). An input force u(t) is applied. The masses of the two carts are M, and M, and their displacements are x(t) and q(t), respectively. The carts are connected by a spring k and a damper b. Answer the following questions: By using Newton's Second Law, derive two mathematical equations that describe the motion of the two carts. (b) Q(s) Hence derive the following two transfer functions: G,(s) =- U(s) (c) x(t) 9(1) k M, M2 u(t) Figure (1b)
Transcribed Image Text:Two carts with negligible rolling friction are connected as shown in Figure (1b). An input force u(t) is applied. The masses of the two carts are M, and M, and their displacements are x(t) and q(t), respectively. The carts are connected by a spring k and a damper b. Answer the following questions: By using Newton's Second Law, derive two mathematical equations that describe the motion of the two carts. (b) Q(s) Hence derive the following two transfer functions: G,(s) =- U(s) (c) x(t) 9(1) k M, M2 u(t) Figure (1b)
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