diff --git a/content/03_oscillation.html b/content/03_oscillation.html index 144e0f2..d338b40 100644 --- a/content/03_oscillation.html +++ b/content/03_oscillation.html @@ -905,15 +905,13 @@ function draw() {
Figure 3.20: On the left, the pendulum is drawn rotated so that the arm is the y-axis. The right shows F_g zoomed in and divided into components F_{gx} and F_{gy}.

The key here is that the top angle of the right triangle is the same as the angle \theta between the pendulum’s arm and its resting position. Just as I demonstrated in the discussion of polar coordinates, the sine and cosine functions allow me to separate out the components of the gravity force (the hypotenuse) according to this angle. For F_{gx}, I need to use sine:

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- Figure 3.21: F_{gx} is now labeled F_p, the net force in the direction of motion. -
Figure 3.21: F_{gx} is now labeled F_p, the net force in the direction of motion.
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\sin(\theta) = F_{gx} / F_g

Solving for F_{gx}, I get this:

F_{gx} = F_g \times \sin(\theta)
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+ Figure 3.21: F_{gx} is now labeled F_p, the net force in the direction of motion. +
Figure 3.21: F_{gx} is now labeled F_p, the net force in the direction of motion.
+

I’ll now rename this force F_p for force of the pendulum. In Figure 3.21, I’ve restored the diagram to its original orientation and relabeled the components. I’ve also moved the starting point of F_p from the bottom of the right triangle to the bob’s center, to clarify how this force moves the bob.

There it is. The net force of the pendulum that causes the rotation is calculated as follows:

F_p = F_g \times \sin(\theta)
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