What is the Differential Equation for This Mechanical System?

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Homework Statement



In this problem I'm asked to give the differential equation of the mechanical system in the following diagram:

http://www.jelp.org/imagenes/mech.jpg

Homework Equations



Once i understand the diagram, i'll get the motion equation by Newton or lagrange. But what is G in the diagram?? I can't ask to the "creator of the draw". Is the black dot fixed? What do you think?? Thanks a lot...
 
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The "squggle" is a spring with spring constant K, the box is a mass. The open box G is a "dash pot" or dampener with dampening constant G (applies a force -G times the velocity) and of course the wall on the right is a wall i.e. fixed point.

I'm not sure about the f(t), whether that is a force or a position x1=f(t). My guess is that it is indeed a force.
 

Thread 'Please tell me where I am going wrong in this integral'

##|\Psi|^2=\frac{1}{\sqrt{\pi b^2}}\exp(\frac{-(x-x_0)^2}{b^2}).## ##\braket{x}=\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dx\,x\exp(-\frac{(x-x_0)^2}{b^2}).## ##y=x-x_0 \quad x=y+x_0 \quad dy=dx.## The boundaries remain infinite, I believe. ##\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dy(y+x_0)\exp(\frac{-y^2}{b^2}).## ##\frac{2}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,y\exp(\frac{-y^2}{b^2})+\frac{2x_0}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,\exp(-\frac{y^2}{b^2}).## I then resolved the two...
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Thread 'Number of quantum accessible states of a particle given T, N?'

It's given a gas of particles all identical which has T fixed and spin S. Let's ##g(\epsilon)## the density of orbital states and ##g(\epsilon) = g_0## for ##\forall \epsilon \in [\epsilon_0, \epsilon_1]##, zero otherwise. How to compute the number of accessible quantum states of one particle? This is my attempt, and I suspect that is not good. Let S=0 and then bosons in a system. Simply, if we have the density of orbitals we have to integrate ##g(\epsilon)## and we have...
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