# finding the equation of a system involving dashpots and mass on wheels

by lzh
Tags: dashpots, equation, involving, mass, wheels
 P: 111 1. The problem statement, all variables and given/known data consider the mechanical system below. Find the equation depicting the system. u is the input force. sorry for the poor picture, I had to draw it on my tablet... Uploaded with ImageShack.us 2. Relevant equations F=ma 3. The attempt at a solution I'm not sure how to treat the dashpot in parallel with the mass. I came up with the following system of equations: 0=k1x+mx"+k2(x-y)+b(x-y) 0=b(x-y)+k2(x-y)+k3(y-u)
 PF Patron HW Helper Sci Advisor Thanks P: 25,521 hi lzh! according to http://en.wikipedia.org/wiki/Dashpot, the resistance is porportional to the speed
 P: 111 hi! oops I mistyped... 0=k1x+mx"+k2(x-y)+b(x'-y') 0=b(x'-y')+k2(x-y)+k3(y-u)
P: 120

## finding the equation of a system involving dashpots and mass on wheels

I can't tell you anything for sure since I haven't done these problems in years. The way I used to check out the mechanical "circuit" when I got overwhelmed was based on my electrical knowledge. Your dashpot is a resistor and your mass is an inductor. Always use this as a double check when you're unsure of a mechanical setup. The info for the electrical setup will always be more easy to find.

EDIT: Looking at your equations of motion now though, I think you have it or are close. There is no need to fudge with the circuit. Just find X and Y based on input u.
 P: 111 0=k1x+mx"+k2(x-y)+b(x'-y') 0=b(y'-y')+k2(y-x)+k3*y+u after some more modification, but i'm still unsure...
 P: 1,115 For starters: Note that u would be a velocity input, not a force input. b is by' - it has no contact with the velocity at x and I think for m it is m(y"-x") I haven't checked your eqautions yet, so patience please

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