Equations of motion for a dual mass-spring-damper

In summary, the conversation discusses deriving equations of motion from a mass-spring-damper diagram and concerns about the correctness of the expressions and signs. The participant also mentions drawing free-body diagrams and setting up equations using the net force. There is also a request to reconsider the extension of the rightmost spring and the direction of the force from the rightmost damper.
  • #1
invariant99
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Homework Statement



We have been given the following mass-spring-damper diagram, and are asked to derive the equations of motion. The positions of the two masses are given as q1 and q2.

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The Attempt at a Solution



I began by drawing free-body diagrams for each mass.

upload_2018-10-11_19-8-17.png


Then I set up the equations using F_net = mq'' = sum of the forces acting on the mass.

upload_2018-10-11_19-9-15.png


How does that look? I'm not very experienced at these, and I'm concerned that I've written some of the expressions incorrectly, and that I have some of the signs wrong as well. Thank you.
 

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  • #2
Think again about the extension of the rightmost spring, and the direction of the force from the rightmost damper.
 

Related to Equations of motion for a dual mass-spring-damper

1. What is a dual mass-spring-damper system?

A dual mass-spring-damper system is a mechanical system that consists of two masses connected by springs and dampers. It is used to model the movement of two connected objects, such as a car suspension or a two-pendulum system.

2. What are the equations of motion for a dual mass-spring-damper system?

The equations of motion for a dual mass-spring-damper system are derived from Newton's second law and include the forces from the springs and dampers. The equations can be written as a system of differential equations and can be solved to determine the positions and velocities of the masses as a function of time.

3. How do the parameters of the system affect the equations of motion?

The parameters of the system, such as the masses, spring constants, and damping coefficients, directly affect the equations of motion. Changing these parameters can alter the behavior of the system, such as the frequency and amplitude of oscillations, and the stability of the system.

4. Can the equations of motion be solved analytically or do they require numerical methods?

The equations of motion for a dual mass-spring-damper system can be solved analytically for simple cases, such as when the system is linear and has no external forces. However, for more complex systems, numerical methods are often required to solve the equations.

5. How are the equations of motion used in real-world applications?

The equations of motion for a dual mass-spring-damper system are used in many real-world applications, such as designing car suspensions, analyzing vibrations in buildings and bridges, and studying the dynamics of two-pendulum systems. They also serve as a fundamental concept in the study of mechanical systems and can be extended to more complex systems with multiple masses and degrees of freedom.

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