Perhaps you might enjoy reading/learning about genetic algorithms, or even broader, Evolutionary Algorithms in Computer Science. Are you familiar with these algorithms? Obviously, I'm still not sure how you can define a "theory" to a computer... but its along the lines of what you are talking...
I mean... there isn't really any shortcut to this (If thats what you are looking for)
You can do (A*B + C*D + E*F)^2 = (A*B + C*D + E*F)*(A*B + C*D + E*F) and just multiply it out term by term.. or you can let a = AB+CD, and b = EF and use the general form for (a+b)^2
so.. (AB + CD)^2...
what are A, B, C, D, and E? Real or complex?
I'm not entirely sure what you mean by "simplify" because it already seems to be in simplified form. Did you mean expand? If you meant expand..
Then use the general {(a +b)}^2 = a^2 +2ab +b^2 ...
let AB+CD =a, and EF = b
Ok, before I attempt to explain it again.. I'll try to show the flaw in your logic (bear with me here).
"The top box cannot have a force higher than 1.715" - this is true
"the bottom box has to overcome 2.95 N" - This is not true. Draw your free-body diagram for the lower box, and you will see...
Mit is pretty cut-throat, it will be awesome if you get in. The problem with Berkeley is that their admission rate is about 80% in-state. Thirdly, Stanford is just amazing. Although these are difficult schools to get in, I think you have a shot.
You should consider Carnegie Mellon, their CS...
ok well... one of the mistakes I see is how you reached the conclusion "3x +2 =3x +2 for all real nobs"
well, this isn't true... is it? ex: x= -1. |3(-1)+2(-1)| does not equal (-1)|3(-1)+2|.
Break it up like this:
{ |3x^2 + 2x|= |x||3x+2| = x |3x + 2| } \Rightarrow { |x|=x , for (3x+2)...
The level of difficulty of a problem does has nothing to do with how confusing the notation is. It seems like you went out of your way to make this problem as confusing as possible.. its not only confusing, but it has several errors. A genuinely difficult math problem will be difficult...
It is very likely that they used wolfram alpha, Mathematica, or MATLAB to solve for the two ODE's: F(z) and G(t). You can let u(0,t) = h(t). Then once u(z,t) is solved for, its not hard to find something like that. But again, I would need to see what their PDE was, and the boundary conditions. I...
I'm guessing that should be 3.43m/s^2? Rounding error perhaps? How did you get this?
Now ma_{net}= F - F_k -F_s , remember you are applying the force on the lower box, so you should know what the value of m is from that.
**edit:
Ok i see how you got 3.10. You did 4.655/1.5; however, you are...
would you mind explaining where the integral comes from and what is that awkward symbol, that sort of looks like the Summation Sign (Sigma)? Moreover, what is f? In general, I can't make any sense of what's going on
You use your initial conditions to find the coefficients A and B. You have the correct value for A, and we see that B is 0. Hence, this X(T)=Asin(wt) satisfies the initial condition X(0)=0. We know X(0)=0 because the problem says the spring is relaxed.
Look at it this way... If it had said the...
Ah, absolutely 4.655 isn't the maximum. I should really be careful when I look at these late at night.. *angry face* :/. F needs to be maximized such that the top box doesn't fall off.
The maximum acceleration so that the top box doesn't fall of is: 1.715 N = 0.5 kg * a, then use that a for...