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

  • Thread starter lzh
  • Start date
  • #1
lzh
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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]

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Homework Equations


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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Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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hi lzh! :smile:

according to http://en.wikipedia.org/wiki/Dashpot" [Broken], the resistance is porportional to the speed :wink:
 
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  • #3
lzh
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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)
 
  • #4
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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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  • #5
lzh
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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...
 
  • #6
256bits
Gold Member
3,223
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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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