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Cycles. So motion that has a repeating pattern is called cyclic motion, also called periodic
motion. So there's lots of examples for such asÉsay wheel thatÕs turning, so it took
completes one cycle when it completes its entire turn. And walking is a also cyclic
motion, so it repeats after two steps. Other examples include the vibration, say mass on
rubber band that's vibrating up and down, and something swinging back and forth like
an oscillating, a pendulum. So vibrations and oscillations are other examples of cyclic,
periodic motion. Now there's some vocabulary that's good to understand when it comes to
a cyclic motion. So the following terms: period, frequency, amplitude and speed. Let's take
a few minutes to define these and explain the relationship between these four elements.
So the simplest one is the period for a cycle, that is the time that it takes to do one full
round trip. So typically this would be measured in seconds, so as an example the period for
a normal walk cycle, would be about one second per cycle, so it will take about one second
to complete two steps: left foot, right foot. Now for rotation, we also talk about the period
of rotation, thatÕs just the time it takes to make one full-turn. You see in this photo,
because of the gearing, the period of rotation for the small wheel would happen to be of
shorter time shorter period than for the large wheel. Now, a closely related topic or element
is the frequency for a cycle. So the frequency is just the inverse of the period. So for
example if we have something which has a period of two seconds per cycle, then the frequency
is a half cycle per second. And frequency, we call cycles per second Hertz. So half a
cycle per second is the same as saying 1/2 Hz. Same concept for rotation, we can talk
about the frequency rotations, so thatÕs the number of turns or revolutions or rotations
per second. Sometimes this is measured in minutes such as rpm, revolutions per minute.
But we are talking about cycles per second in the this example here, if the tops are
spinning 20 revolutions per second then that's a frequency of 20 Hz, the corresponding period
is the inverse of that so it takes 1/20th of a second to make one revolution. The next
element is the amplitude. So when we have cyclic motion, the amplitude is the distance
of from the center position for the motion. So for a walk cycle we can define the amplitude
as being the stride length. So thatÕs the distance for two steps. For rotation, the
distance that we would be interested in and looking at would be the radius of the rotation.
So in this wheel, we might be interested in the radius of the inner wheel or the radius
of the outer wheel when we're looking at the rotation. For the merry-go-round, we might
be interested in the motion for the horses towards the inside of the track or the horses
outside of the track. Of course when the merry-go-round circles, the horses all travel together in
terms of revolutions but the horses on the inside of the track don't travels as far as
the ones on the outside of the track. And we see this because the inner radius has a
smaller circumference, and the outer radius is a larger circumference. So we can define
the amplitude for a cycle in the rotation as the circumference for the rotation. Of
course, circumference and radius are closely related, circumference is 2pi x radius, basic
geometry. Now the last element that we care about in terms of periodic or cyclic motion
is the speed of the motion. Now the speed of the motion depends on both frequency and
amplitude. So the larger the frequency or the larger the amplitude, the faster the motion.
In fact, the speed is defined as the amplitude times the frequency, which is the same thing,
the amplitude is divided by period. So for walking, let's say that you are walking slowly,
and you have a stride length, that would be the amplitude, letÕs say we have the stride
length of 3 feet and the frequency is that you're taking 2 strides every three seconds.
Well if that's the case then you are traveling at a speed of 2 feet per second. That's about
1/3 miles per hour. On the other hand, the faster walk might have a longer stride and
also a quicker cadence, or a faster strike rate. So if you have a strike length of 4
feet, and a stride rate of one stride per second, then you're traveling at a speed which
is 4 feet per second which is as twice what the slow walk was. So thatÕs just an example
of how speed is related to both amplitude, and frequency for cyclic motion. Now I want
to point out that you should not confuse frequency of the cycle with the speed of the motion.
We just saw that two are related but they're not the same thing. So letÕs take a look
at this example, these dogs, as they're walking along, if they walk together then they are
all going at the same speed, but the small dogs have a short leg, so they take short
steps, or short stride. So in order to move the same speed, their strike rate has to be
higher. So they take more steps per second, nevertheless all the dogs are traveling at
the same speed. Anyway, I just want to emphasize the distinction between frequency of the cycle
and the speed of motion. And finally talk about rotation, the speed of rotation is larger
for a point on the outer rim compared with the point on the inner rim. So these two points
complete one cycle in the same amount of time, but because the circumference is larger for
the point on the outer rim, it's traveling at a higher speed than the point on the inner
rim. Same thing with the merry-go-round horses on the outer rim are traveling at a higher
speed than the inner rim even though it takes the same time to go one cycle around, one
rotation around the merry-go-round. So in the summary, motion that has a repeating pattern
is called cyclic motion or periodic motion. The time it takes to complete one full cycle
is called period. Frequency is the inverse of the period, so thatÕs the number cycles
per second, usually expresses as hertz, which is the same cycles per second. The amplitude
indicates the size of the motion. So for example the stride length in the walk cycle. For rotation,
the amplitude would be the circumference that were traveling as we move around in a circle,
and of course that depends on the radius of rotation. So that's the basic vocabulary for
cyclic motion, and one last thing: donÕt forget that the speed of the motion increases
with both amplitude and frequency. So obviously, period and frequency are closely related.
Speed is closely related to amplitude and frequency. Anyway, we will use these ideas
quite a bit because there's quite a bit of motion in animation which is cyclic. So see
you then.