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

## Homework Statement

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...
http://img685.imageshack.us/img685/1043/ogataprob.png [Broken]

F=ma

## 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)

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tiny-tim
Homework Helper
hi lzh!

according to http://en.wikipedia.org/wiki/Dashpot" [Broken], the resistance is porportional to the speed

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hi!
oops I mistyped...
0=k1x+mx"+k2(x-y)+b(x'-y')
0=b(x'-y')+k2(x-y)+k3(y-u)

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.

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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...

256bits
Gold Member
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")