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In this system, there are two mass elements: m, and m₂. They are con- nected by a spring. m₁ is also connected to a massless rod, which can rotate at its midpoint. The other end of this massless rod is connected to another massless rod, which is connected to the ground through a spring and a damper. This configuration forms the basis of the system. You may assume small deflections for this problem and that the vertical connections are rigid links. When the coordinates y₁, 92, y are equal to zero, the gravi- tational force on the masses is covered by springs (the system is at its static deflection). Two input forces, fi and f2, are applied on the masses m₁ and m2 respectively. HINT: You should not consider the gravity force in your solution. Your tasks: A Short Answer: Which elements (refer to them by their corresponding constants) can store or possess energy in this system? B Draw the FBD for each mass (one for each of m₁ and m2. C Derive the equations of motion for the masses with y₁ and y2 as the dynamic variables. Please put the dynamic variables on the left- hand side and the input terms on the right-hand side. = D BONUS: If the system is at an instantaneous condition where yı 1 [m/s], 1 = Ÿ2 2 = 1 [m/s2], f₁ = 1 [N], f2 = 3 [N], m₁ = 1 [N/m], c= 1 [Ns/m]. m₂ = 1 [kg], k₁= k2 deflection in spring k₁? What is the =

In this system, there are two mass elements: m, and m₂. They are con- nected by a spring. m₁ is also connected to a massless rod, which can rotate at its midpoint. The other end of this massless rod is connected to another massless rod, which is connected to the ground through a spring and a damper. This configuration forms the basis of the system. You may assume small deflections for this problem and that the vertical connections are rigid links. When the coordinates y₁, 92, y are equal to zero, the gravi- tational force on the masses is covered by springs (the system is at its static deflection). Two input forces, fi and f2, are applied on the masses m₁ and m2 respectively. HINT: You should not consider the gravity force in your solution. Your tasks: A Short Answer: Which elements (refer to them by their corresponding constants) can store or possess energy in this system? B Draw the FBD for each mass (one for each of m₁ and m2. C Derive the equations of motion for the masses with y₁ and y2 as the dynamic variables. Please put the dynamic variables on the left- hand side and the input terms on the right-hand side. = D BONUS: If the system is at an instantaneous condition where yı 1 [m/s], 1 = Ÿ2 2 = 1 [m/s2], f₁ = 1 [N], f2 = 3 [N], m₁ = 1 [N/m], c= 1 [Ns/m]. m₂ = 1 [kg], k₁= k2 deflection in spring k₁? What is the =

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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In this system, there are two mass elements: m₁ and m₂. They are con- nected by a spring. m₁ is also connected to a massless rod, which can rotate at its midpoint. The other end of this massless rod is connected to another massless rod, which is connected to the ground through a spring and a damper. This configuration forms the basis of the system. You may assume small deflections for this problem and that the vertical connections are rigid links. When the coordinates y₁, y2, y are equal to zero, the gravi- tational force on the masses is covered by springs (the system is at its static deflection). Two input forces, fi and f2, are applied on the masses m₁ and m2 respectively. HINT: You should not consider the gravity force in your solution. Your tasks: A Short Answer: Which elements (refer to them by their corresponding constants) can store or possess energy in this system? B Draw the FBD for each mass (one for each of m₁ and m₂. H C Derive the equations of motion for the masses with y₁ and y2 as the y₂ dynamic variables. Please put the dynamic variables on the left- hand side and the input terms on the right-hand side. D BONUS: If the system is at an instantaneous condition where yı 1 [m/s], ₁ = 2 = 1 [m/s²], f₁ = 1 [N], 1 [N], f2 = 3 [N], m₁ = What is the 1 [kg], k₁= k₂= 1 [N/m], c = 1 [Ns/m]. deflection in spring k₁? m2 kı = У1' = fil m₁ M₂ f2 a K₂ a H ww k₁ JC Figure 1: System schematic. y
Transcribed Image Text:In this system, there are two mass elements: m₁ and m₂. They are con- nected by a spring. m₁ is also connected to a massless rod, which can rotate at its midpoint. The other end of this massless rod is connected to another massless rod, which is connected to the ground through a spring and a damper. This configuration forms the basis of the system. You may assume small deflections for this problem and that the vertical connections are rigid links. When the coordinates y₁, y2, y are equal to zero, the gravi- tational force on the masses is covered by springs (the system is at its static deflection). Two input forces, fi and f2, are applied on the masses m₁ and m2 respectively. HINT: You should not consider the gravity force in your solution. Your tasks: A Short Answer: Which elements (refer to them by their corresponding constants) can store or possess energy in this system? B Draw the FBD for each mass (one for each of m₁ and m₂. H C Derive the equations of motion for the masses with y₁ and y2 as the y₂ dynamic variables. Please put the dynamic variables on the left- hand side and the input terms on the right-hand side. D BONUS: If the system is at an instantaneous condition where yı 1 [m/s], ₁ = 2 = 1 [m/s²], f₁ = 1 [N], 1 [N], f2 = 3 [N], m₁ = What is the 1 [kg], k₁= k₂= 1 [N/m], c = 1 [Ns/m]. deflection in spring k₁? m2 kı = У1' = fil m₁ M₂ f2 a K₂ a H ww k₁ JC Figure 1: System schematic. y
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