Is \( x_0 \cos(\theta) \) Misinterpreted in Radial Coordinates?

[SlowProgress]

Homework Statement

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/8-03-physics-iii-vibrations-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.

 

[CAF123]

x = x_ocos(wt + δ) describes SHM with maximal amplitude x_o(since cos never exceeds 1). Since the cos function is periodic, he represented the function as a circle with radius x_o, the max amplitude. The projection of x_o onto the x-axis is the x_ocosθ.

This is similar to how sin and cos are defined via the unit circle, except here the circle is not of radius unity.

 

[SlowProgress]

The projection of x_o onto the x-axis is the x_ocosθ.

This is similar to how sin and cos are defined via the unit circle, except here the circle is not of radius unity.

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?

 

[SlowProgress]

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.

 

[CAF123]

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.

Yes, any point lying on the circle is a distance x_o away from the origin.