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## Homework Statement

This was supposed to be an easy question. I have a question here that wants you to describe a yoyo's acceleration (in one dimension) using Lagrangian mechanics. I did and got the right answer. Now I want to use Hamilton's equations of motion but I get a wrong number. Here is the excerpt

"

*A yoyo attached to a mass less string is suspended vertically from a fixed point and the other end is wrapped several times around a uniform cylinder of mass, m and radius R. When the cylinder is released it moves vertically down, rotating as the string unwinds. Write down the Lagrangian equation using the distance x as your generalized coordinate. Find the Lagrange equation of motion and show that the cylinder accelerates downward with*#\ddot{x}# = 2g/3"

## Homework Equations

I used Hamilton equation xdot = partial H/partial P

To help,

L = (3/4) m xdot^2 + mgx

and

H = (3p^2)/(4m) - mgx

## The Attempt at a Solution

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I used Hamilton's equation and took the derivative

d/dt (xdot) = xddot = d/dt(3p/4m)

xddot = (3 xddot)/2