10.9#8

I assume this attached the list of all of the answers that I've put in so far. Here's the rest of what was in the email:

For part B, I was able to solve the magnitude of the force by using rotational formulas from the physics class I took last semester. I found that to be 17.55 N.

Back to part A, looking in the textbook, I found what I believe the relevant equation to be:
F(t) = - m * w^2 * (a * cos(w * t) i + a * sin(w * t) j)

I have tried plugging in everything, leaving t in the expression, and I also tried plugging in 12 for t. WeBWork says I'm wrong for both. Here's my work for the x-component:
w = 2pi / 12 = pi/6
a = w^2 / r
F(t) = - 8 * (pi/6)^2 * ((pi/6)^2 / 8) * cos(pi/6 * t)
F(t) = - (pi/6)^2 * (pi/6)^2 * cos(pi/6 * t)
F(t) = - (pi/6)^4 * cos(pi/6 * t)
Is there something else I'm supposed to do after this point?

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(nope, it doesn't attach everything you've done, I just get to see that last thing you did)

Ok, looks like you started off sort of in the right direction, in that you start with a correct vector equation for F=-mw^2(a*cos(wt) i + a sin(wt)j),  but then a) got yourself tangled up figuring out what to put in for w and a (and it looks like you kind of got some of that stuff correct but were insecure about it and kept going when you should have stopped) and then b) you forgot that F is a vector and only kept the i component.

And if not for those confusions you could have worked it out that way.  But I propose that you take a step back and remember Newton's Law, which is covered in the textbook and says that F=ma; note that these are vector equations. And we talked in class about the fact that the acceleration vector a is the second derivative of the position r.  So the basic thing for you to know is: what does it take for you to make r(t) travel around a circle of radius 8 in 12 seconds?  (the w=2pi/12 you have is correct and plays into it).  Once you have that, take the derivative of it twice correctly, using the chain rule of differentiation, and multiply by the mass to get the force. Note that the force will have two nonzero components, and that they will both depend on time through the parameterization r(t)  you  used.