- #1
jorgen
- 14
- 0
Hi all,
I have to determine the mean elongation of a spring with temperature. The spring constant is alpha and the gravitational acceleration is g. I have the following expression for the force
[tex]F = -\alpha*x +m*g[/tex]
which I can integrate for an expression of the energy
[tex]E = \frac{-\alpha*x^2}{2}+m*g*x[/tex]
I can factorize this into
[tex]E = (x-\frac{m*g}{\alpha})^2[/tex]
than I would like to put it into the Boltzman distribution getting the partition function and from that determine the mean elongation
[tex]Z = \int_{-\infty}^{\infty}exp(-E*\beta)[/tex]
but this gives me infinity - any help or advice appreciated thanks in advance,
Best
J
I have to determine the mean elongation of a spring with temperature. The spring constant is alpha and the gravitational acceleration is g. I have the following expression for the force
[tex]F = -\alpha*x +m*g[/tex]
which I can integrate for an expression of the energy
[tex]E = \frac{-\alpha*x^2}{2}+m*g*x[/tex]
I can factorize this into
[tex]E = (x-\frac{m*g}{\alpha})^2[/tex]
than I would like to put it into the Boltzman distribution getting the partition function and from that determine the mean elongation
[tex]Z = \int_{-\infty}^{\infty}exp(-E*\beta)[/tex]
but this gives me infinity - any help or advice appreciated thanks in advance,
Best
J