So let's call Aw^2 k for simplicity
P is -ksin(2wt)/2
P' is -k/4cos(2wt)
We need to find where cos is -1 so P is positive and maximized. This occurs at 3pi\2
2wt = 3pi\2
w = 3pi\4t
1/T= 2pi\
T = 3\8t
I thought
1) no external forces
2) no external torque
3) energy loss due to heat/friction inside the block
So the fact that there's an energy loss due to thermal energy negates everything?
Ya I see that but isn't it root(GM/a), where a is the semi major axis for object B. Doesn't that mean that the radius in the numerator won't cancel with the semi major axis on the denominator?
That's where I was worried.
Ya I see why. It's because it takes T/4 to get to the mean. T/4 to get to the right extreme, and then the reverse to get back. So it makes sense that its T/4.
What's next?
Well if A is the amplitude, I would think that as one block is X to the right, the other would be A-X to the left. The spring is stretched by A-X + X = A? The force that the spring exerts on the right-hand block I'm not sure how to write.
tanθ = b/a
Ahh, now I can solve the problem.
I found before that Ff > mgsinθ
umgcosθ > mgsinθ
u > tanθ
u > b/a
This is correct.
Thanks so much. Not only were you EXTREMELY helpful, but you helped me in a very timely fashion. Your help is greatly appreciated.
Ok so the main concepts in the...