Find the Lagrangian of this single mass system

[MyoPhilosopher]

Homework Statement

Find the lagrangian of the following system (pic included below)

Relevant Equations

L = T - U

 

[BvU]

Is there a question in this ?

 

[MyoPhilosopher]

Is there a question in this ?

sorry, is my Langragian set up and equations correct?

 

[BvU]

Did you check them thoroughly ? That should be enough, shouldn't it ?

 

[MyoPhilosopher]

Did you check them thoroughly ? That should be enough, shouldn't it ?

Thanks for the help

 

[ehild]

sorry, is my Langragian set up and equations correct?

What does it mean that the springs have zero equilibrium lengths?
What is the elastic potential energy?

 

[MyoPhilosopher]

What does it mean that the springs have zero equilibrium lengths?
What is the elastic potential energy?

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

 

[ehild]

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

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?

 

[BvU]

Zero equilibrium length means spring energy is zero at spring length zero. Unrealistic, but pobably set like that to make it easier for you !

 

[MyoPhilosopher]

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?

I assumed the unstreched length of each spring was L/2. 1/2 * k(Δx)^2

 

[MyoPhilosopher]

Zero equilibrium length means spring energy is zero at spring length zero. Unrealistic, but pobably set like that to make it easier for you !

Alright so my equations for potential should quite literally use the (ΔLength = current length). so essentially 0.5k(0-currentl length)^2

 

[BvU]

That is my interpretation, yes.

 

[BvU]

Quesion: why did you choose the origin like that, instead of at the very center ?

 

[MyoPhilosopher]

That is my interpretation, yes.

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?

 

[MyoPhilosopher]

Quesion: why did you choose the origin like that, instead of at the very center ?

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.