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A dual mass-spring-damper system is shown in the diagram below. Consider the system given in Figure 1. Three springs are connected to a mass and to a fixed support, configured as shown. When the coordinate ₁ is equal to zero, there is no spring force. Two input forces F₁ and F2, are applied on the masses my and m₂ as shown. There is a damper between the two masses. Your tasks: k₁ k3 m₁ F₁ X1 + C Figure 1: System schematic. M₂ F2 X2 A Short Answer: Which elements (refer to them by their corresponding constants) can store or possess energy in this system? B Combine the springs into one equivalent spring with spring constant keq and write it in terms of (k, ke, ks). Recall that for series springs, 1/keq,series = 1/k₁ + 1/k₂. C Draw the FBD for each mass (one for m₁, one for m2) D Derive the equations of motion for the masses with a, and 2 as the dynamic variables E BONUS: If the system is static (all time derivatives of ₁, 2 equal to zero), k₁ = k₂= k = 2 [N/m], F₂ = 0 [N], and F₁ = 3 [N], what is the force in spring k₁?

A dual mass-spring-damper system is shown in the diagram below. Consider the system given in Figure 1. Three springs are connected to a mass and to a fixed support, configured as shown. When the coordinate ₁ is equal to zero, there is no spring force. Two input forces F₁ and F2, are applied on the masses my and m₂ as shown. There is a damper between the two masses. Your tasks: k₁ k3 m₁ F₁ X1 + C Figure 1: System schematic. M₂ F2 X2 A Short Answer: Which elements (refer to them by their corresponding constants) can store or possess energy in this system? B Combine the springs into one equivalent spring with spring constant keq and write it in terms of (k, ke, ks). Recall that for series springs, 1/keq,series = 1/k₁ + 1/k₂. C Draw the FBD for each mass (one for m₁, one for m2) D Derive the equations of motion for the masses with a, and 2 as the dynamic variables E BONUS: If the system is static (all time derivatives of ₁, 2 equal to zero), k₁ = k₂= k = 2 [N/m], F₂ = 0 [N], and F₁ = 3 [N], what is the force in spring k₁?

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
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A dual mass-spring-damper system is shown in the diagram below. Consider the system given in Figure 1. Three springs are connected to a mass and to a fixed support, configured as shown. When the coordinate ₁ is equal to zero, there is no spring force. Two input forces F₁ and F2, are applied on the masses m₁ and m₂ as shown. There is a damper between the two masses. لشميشة k3 M₁ F₁ X1 + с Figure 1: System schematic. M₂ F₂ X2 Your tasks: A Short Answer: Which elements (refer to them by their corresponding constants) can store or possess energy in this system? B Combine the springs into one equivalent spring with spring constant keq and write it in terms of (k₁, ka, ks). Recall that for series springs, 1/keq, series = 1/k₁ + 1/k₂. C Draw the FBD for each mass (one for my, one for m₂) D Derive the equations of motion for the masses with , and 2 as the dynamic variables E BONUS: If the system is static (all time derivatives of ₁, 2 equal to zero), k₁=k₂= k = 2 [N/m], F₂ = 0 [N], and F₁ = 3 [N], what is the force in spring ki?
Transcribed Image Text:A dual mass-spring-damper system is shown in the diagram below. Consider the system given in Figure 1. Three springs are connected to a mass and to a fixed support, configured as shown. When the coordinate ₁ is equal to zero, there is no spring force. Two input forces F₁ and F2, are applied on the masses m₁ and m₂ as shown. There is a damper between the two masses. لشميشة k3 M₁ F₁ X1 + с Figure 1: System schematic. M₂ F₂ X2 Your tasks: A Short Answer: Which elements (refer to them by their corresponding constants) can store or possess energy in this system? B Combine the springs into one equivalent spring with spring constant keq and write it in terms of (k₁, ka, ks). Recall that for series springs, 1/keq, series = 1/k₁ + 1/k₂. C Draw the FBD for each mass (one for my, one for m₂) D Derive the equations of motion for the masses with , and 2 as the dynamic variables E BONUS: If the system is static (all time derivatives of ₁, 2 equal to zero), k₁=k₂= k = 2 [N/m], F₂ = 0 [N], and F₁ = 3 [N], what is the force in spring ki?
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