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

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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PARTS A & B solve carefully and label each part and CIRCLE FINAL ANSWER ( Use image Below) Part A - Assuming the elements are all linear, determine a model for the mass-spring-damper system. Make sure to clearly define the direction of positive velocity. Simplify your answer such that the model is in terms of the parameters (?, ?, ??, ??), the input force (?), the spring deflection and the mass velocity as well as their time derivatives. Part B - Take the ANSWER from PART A and replace the damping constant ? with the nonlinear expression ? = ?? + ?? + ? , with ? as the velocity of the mass.
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Can you please show the complete solution and free body diagram of the image below. Thanks! Subject: Mechanical Vibration
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