The system examined in the problem is depicted below:(adsbygoogle = window.adsbygoogle || []).push({});

^^^^^(m1)^^^^^(m2)

m1 and m2 are connected by a spring and m1 is connected to the wall by a spring. The spring constant is k.

T = m/2 [ x1'^2 +x2'^2 ] kinetic energy of system (x1' is velocity of m1, x2' is velocity of m2)

U = 1/2 m k^2 (x1 - b)^2 + 1/2 m k^2 (x2-x1-b)^2 potential energy of system (x1 is position of m1, x2 is position of m2, b is the unstretched length of the spring)

Is m the reduced mass?

Also, could someone explain how the equation for U is derived? Why is it k^2 and not just k (i.e. potential energy for spring = 1/2 kx^2)? Also, why is there a mass term in the potential energy? Or is this the wrong expression for potential energy altogether?

I known then that the Lagrangian for the system is L = T - U. I can then take derivatives and substitute into the Euler-Lagrange equation. I should have two E.L. equations, correct? But what should I solve for -- x1 and x2?

Any guidance/hints greatly appreciated!

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# Homework Help: Lagrangian for system with springs

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