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MyoPhilosopher
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- Homework Statement
- Find the lagrangian of the following system (pic included below)
- Relevant Equations
- L = T - U
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sorry, is my Langragian set up and equations correct?BvU said:Is there a question in this ?
Thanks for the helpBvU said:Did you check them thoroughly ? That should be enough, shouldn't it ?
What does it mean that the springs have zero equilibrium lengths?MyoPhilosopher said:sorry, is my Langragian set up and equations correct?
1. I understand it as that at the mass in the center of the blocks and at y=0 in my pic, and lengths L/2 for each spring, is 0 equilibriumehild said:What does it mean that the springs have zero equilibrium lengths?
What is the elastic potential energy?
Zero equilibrium length means zero length when the spring is unstretched. You assumed that the unstretched length is L.MyoPhilosopher said:1. I understand it as that at the mass in the center of the blocks and at y=0 in my pic, and lengths L/2 for each spring, is 0 equilibrium
2. I have the two elastic PEs in the post above individually
I assumed the unstreched length of each spring was L/2. 1/2 * k(Δx)^2ehild said:Zero equilibrium length means zero length when the spring is unstretched. You assumed that the unstretched length is L.
What is the formula for the potential energy of a spring?
Alright so my equations for potential should quite literally use the (ΔLength = current length). so essentially 0.5k(0-currentl length)^2BvU said:Zero equilibrium length means spring energy is zero at spring length zero. Unrealistic, but pobably set like that to make it easier for you !
That makes sense thank you I misread and misunderstood that. Can I ask why the momentum of the mass or object is not conserved? Would be due to constantly changing velocities of the object?BvU said:That is my interpretation, yes.
My first attempt was using polar coordinates but that did not work easily. I chose those points to get a clear x_dot and y_dot for my kinetic energy.BvU said:Quesion: why did you choose the origin like that, instead of at the very center ?
The Lagrangian of a single mass system is a mathematical function that describes the dynamics of the system in terms of its position and velocity. It is used in classical mechanics to derive the equations of motion for the system.
The Lagrangian of a single mass system is calculated by taking the difference between the kinetic energy and potential energy of the system. This can be expressed as L = T - V, where T is the kinetic energy and V is the potential energy.
The Lagrangian of a single mass system is useful because it simplifies the process of finding the equations of motion for the system. It allows for a more elegant and efficient approach to solving problems in classical mechanics.
Yes, the Lagrangian of a single mass system can be used for any type of system, as long as it can be described in terms of position and velocity. It is a general method that can be applied to a wide range of physical systems.
One of the main advantages of using the Lagrangian over other methods is that it takes into account all the forces acting on the system, rather than focusing on individual forces. This makes it particularly useful for systems with complex interactions between different components.