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## Homework Statement

a bead is constrained to move on a wire: y=acosh(x/a).

write the kinetic energy and the potential energy using the coordinates:

1) x

2) l - the length of a curve

**2. The attempt at a solution**

1) is simple:

the kinetic energy in cartesian coordinates is 0.5([tex]\dot{x}[/tex]^2+[tex]\dot{y}[/tex]^2)

and using y=acosh(x/a) I get the following expression

0.5m[tex]\dot{x}[/tex]^2(cosh(x/a)^2

the potential energy is mgh = mgy=mgcosh(x/a).

2) l=integral(dl)=integral[0-->x]{sqrt[(1+(dy/dx)^2)]dx}=asinh(x/a).

so the kinetic energy is 0.5m[tex]\dot{l}[/tex]^2=0.5m[tex]\dot{x}[/tex]^2(cosh(x/a)^2

but what is the expression for the potential energy here? how do I express h?