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

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lzh
#1
Jun4-11, 01:02 PM
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...


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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)
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tiny-tim
#2
Jun4-11, 03:54 PM
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tiny-tim's Avatar
P: 26,158
hi lzh!

according to http://en.wikipedia.org/wiki/Dashpot, the resistance is porportional to the speed
lzh
#3
Jun4-11, 10:21 PM
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)

Jupiter6
#4
Jun5-11, 03:15 AM
P: 128
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.
lzh
#5
Jun5-11, 06:57 PM
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...
256bits
#6
Jun6-11, 09:04 AM
P: 1,414
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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