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16.6 Uniform Circular Motion and Simple Harmonic Motion
The pendulum's displacement is a function of time.
The motion of the pendulum is a function of time.
The ruler has a higher force for the same amount of displacement.
It hurts more when the ruler snaps your hand.
You are observing something.
One way you could decrease the system's maximum speed is to identify it.
You can increase the mass of the object.
There is an easy way to produce simple motion.
The shadow of a ball is projected on the floor by a rotating vertical turntable.
Hooke's law doesn't usually describe systems with large visible displacements.
Simple motion produced in this manner can give a lot of insight into many aspects of waves and oscillations.
Some of the major features of this relationship will be indicated in our brief treatment.
The shadow of a ball on a turntable goes back and forth in a simple motion.
The figure shows the relationship between the two motions.
The point P is traveling around the circle.
The object on the merry-go-round is similar to the point P. The projection of the position of P onto a fixed axis is similar to the shadow of an object.
The projection moves to the left at the time shown in the figure.
The point P around the circle is equal to the point on the - axis.
A point P is moving on a circular path.
The point around the circle and its projection are shown.
The velocities form a triangle similar to the displacement triangle.
The time for one revolution is when the radians are at their highest.
We can use Figure 16.19 to do some further analysis of uniform circular motion.
It is possible to get all of the characteristics of simple motion from an analysis of the projection.
Let's take a look at the period of the projection.
The point P is needed to complete one revolution.
The time is divided by the speed around the circle.
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