Homework Help: (x sub 0)(cosine theta)

1. The problem statement, all variables and given/known data
At 16:30 he writes (x sub 0)(cosine theta). Is x sub 0 the vertical component length of the position vector of the particle? When he labels x sub 0 a little while before, it looks as though x sub 0 is at the radial point along the x axis. How can you use x sub 0 cosine theta at the radial point along the x axis when the position of the particle doesn't coincide with the point at axis?

http://ocw.mit.edu/courses/physics/...and-waves-fall-2004/video-lectures/lecture-1/

Also, I know this doesn't adhere to the default question set-up guidelines, but how would I go about properly asking a question like this? I don't do schoolwork. I study what my weak mind can grasp alone at a pace at which I find most comfortable. I really don't know what he meant by this.

 

But how is the projection of the maximal amplitude on the the x axis x_ocosθ? I thought you use cosine when you want to determine vector components that make up the position of a point along the circle.

He says in the video that to determine the position of the particle along the x axis, you need to take the maximal amplitude times the cosine of theta. Why? What does radius have to do with the position along the x axis which outlines both vector components? Can you try to break this down and explain the intuition even further?

 

Wait does x_0 apply to all radii within the circle? Did he just indicate that the radius, not at the specific spot along the x axis, is x_0? If this is the case, I understand my confusion. And the formula just happens to work now.