Consider a bead of mass m sliding down a wire from the point P (xo, yo). %3D 1. Write and expression for the total time T it takes for the bead to slide from P to the origin as a functional of the path of the wire y(x). 2. Write the Euler-Lagrange equations for the solution. 3. Show that the solution is a a cycloid (or solve the problem directly).
Consider a bead of mass m sliding down a wire from the point P (xo, yo). %3D 1. Write and expression for the total time T it takes for the bead to slide from P to the origin as a functional of the path of the wire y(x). 2. Write the Euler-Lagrange equations for the solution. 3. Show that the solution is a a cycloid (or solve the problem directly).
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Transcribed Image Text:Consider a bead of mass m sliding down a wire from the point P = (xo, yo).
1. Write and expression for the total time T it takes for the bead to slide from P to
the origin as a functional of the path of the wire y(x).
2. Write the Euler-Lagrange equations for the solution.
3. Show that the solution is a a cycloid (or solve the problem directly).
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