- #1

LagrangeEuler

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## Homework Statement

Two pendulums of same mass and length that oscillate in same horizontal plane are connected with maseless horizontal rope. What is dependence of amplitude of pendulums as a function of time?

## Homework Equations

For harmonic oscilation

[tex]x=x_0\sin(\omega t+\varphi_0) [/tex]

Kinetic energy

[tex]E_k=\frac{1}{2}mv^2[/tex]

Potential energy

[tex]E_p=\frac{1}{2}kx^2[/tex]

## The Attempt at a Solution

In case from the problem I suppose that kinetic energy is simple

**[tex]E_k=E_{k1}+E_{k2}=\frac{m}{2}(\dot{\varphi}_1^2+\dot{\varphi}_2^2)l^2[/tex]**

and potential energy is

**[tex]E_p=E_{p1}+E_{p2}=mgl(1-\cos\varphi_1)+mgl(1-\cos \varphi_2)[/tex]**

However I am not sure how from this to get amplitude dependence of pendulums as a function of time.

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