Lagrangian equation for unconstrained motion

[heycoa]

Homework Statement

Write down the Lagrangian for a one-dimensional particle moving along the x-axis and subject to a force: F=-kx (with k positive). Find the Lagrange equation of motion and solve it.

Homework Equations

Lagrange: L=T-U (kinetic energy - potential energy)

The Attempt at a Solution

All i really need help with is finding the potential energy in this problem. I believe that the kinetic energy is T=(1/2)*m*x', where x' is d/dt(x). I don't understand how to get the potential energy out of that force. Please help, thank you.

 

[George Jones]

How do you go from potential energy to force?

Do recognizes the force equation that you have been given?

 

[heycoa]

The force equation looks like that of a spring. But as far as I can remember, you go from potential energy to force by multiplying the force by the distance. This problem just seems weird to me.

 

[George Jones]

The force equation looks like that of a spring.

Yes. What is the potential energy for a spring?

But as far as I can remember, you go from potential energy to force by multiplying the force by the distance.

No, it is the other way around, and also the infinitesimal version.

Do have a textbook that you can read?

 

[A2Airwaves]

Homework Statement

Write down the Lagrangian for a one-dimensional particle moving along the x-axis and subject to a force: F=-kx (with k positive). Find the Lagrange equation of motion and solve it.

Homework Equations

Lagrange: L=T-U (kinetic energy - potential energy)

The Attempt at a Solution

All i really need help with is finding the potential energy in this problem. I believe that the kinetic energy is T=(1/2)*m*x', where x' is d/dt(x). I don't understand how to get the potential energy out of that force. Please help, thank you.

I'm currently working on the exact same question, and using : $$-\frac{\partial U}{\partial x} = F$$ I integrated $F=-kx$ and got : $$T= \frac{1}{2}m\dot{x}^{2},U = kx^{2}$$

Is this correct?
Is T=(1/2)mv^2 always what you substitute in for a simple kinematics question?

 

[vela]

No, that's not correct. The integral of $x$ is $\frac 12 x^2$.

 

[A2Airwaves]

No, that's not correct. The integral of $x$ is $\frac 12 x^2$.

Thank you for the correction, I was able to get the problem right :)