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vs74043

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## Homework Statement

The scenario is a pendulum of length

*l*and mass

*m*attached to a mass of

_{2}*m*which is allowed to slide along the horizontal with no friction. The support mass moves along in the

_{1}*X*direction and the pendulum swings through the x-y plane with an angle θ with the vertical. After finding the Lagrangian and the Euler-Lagrange equations for each of the two variables

*X*and θ, apply the conditions

$$\theta(0)=\theta_{0}<<1\text{ but greater than 0}\\

\dot{\theta}(0)=0\\

X(0)=0\\

\dot{X}(0)=0$$

to get the motion for θ and

*X*.

## Homework Equations

I have derived the Lagrangian of this to be

$$L=\frac{1}{2}(m_{1}+m_{2})\dot{X}^{2}+m_{2}l\cos\theta\dot{\theta}\dot{X}+\frac{1}{2}m_{2}l^{2}\dot{\theta}^{2}+m_{2}gl\cos\theta$$

## The Attempt at a Solution

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