Thursday, November 15, 2007
Problem 8/130
On this problem I am confused as to how we can solve it down to the x(t) with that we have covered thus far. We can't knock out the mg that comes from xstat * k because the other mg is tied up in the fricton term. That is unless we can assume that xstat and friction are equat to zero up and until the slide point.
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7 comments:
I didn't write my friction force in terms of mu and mg. I just left it as f. Then, when I summed the moments about O, I was able to write f in terms of m and x_dot_dot so the f term doesn't show up in the EOM. My EOM turned out to be 1.5mx_dot_dot + kx = 0. But, I'm stuck after this point (I'm not sure that that is the correct EOM, either). I found lamda^2 to be -2k/3m and that's as far as I've gotten.
--to lemerson--
Please see Andrew Crandall's comment. He outlines a good plan.
But the problem with my plan is I only make it half way through the problem. Once I have the EOM, where do I go from there to find the amplitude? I know that the amplitude is the constant that goes in front of sine/cosine term...but other than that, I'm stuck.
--to andrew crandall--
You are on your way there. The EOM looks correct.
* You need to find the natural frequency using your roots for lambda.
* You need to find the response x(t) by enforcing the initial conditions of x(0) = x0 and x_dot(0) = 0.
* You need to solve for the friction force using either your summation of forces or summation of moments equation.
* Then find the largest x0 for which the maximum friction force during one cycle does not exceed mus*N.
--to Andrew Crandall--
(You slipped in your comment before I was done with mine to you ...)
Read over my comment where you are to use the initial conditions to find the response. Let us know if that does not help.
I manage to reach the EOM and was on my way to solve it,but what does x_dot(0) = 0 do?
In order to find the response x(t), you need to impose two initial conditions on the general form of the response x(t) = C*cos(omegan*t) + S*sin(omegan*t) to find C and S.
You are wanting to relate the amplitude of response to the friction force. One way to get a response amplitude of x0 is to start out the system from rest (x_dot(0) = 0) with an initial displacement of x(0) = x0. These are the two initial conditions that you will use to find the response.
Let us know if that does not help.
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