Contenuto principale

## Interpreting the periodicity of algebraic models

Ora corrente:0:00Durata totale:3:21

# Periodicity of algebraic models

## Trascrizione del video

- [Voiceover] We're told Divya
is seated on a Ferris Wheel at time t equals zero. The graph below shows her height h in meters, t seconds
after the ride starts. So at time equals zero, she
is, looks like about two, what is this, this
would be one and a half, so it looks like she's about
two meters off the ground and then as time
increases, she gets as high as, it looks like this is
close to 30, maybe 34 meters and then she comes back
down, looks like two meters and up to 34 meters again,
so let's read the question. So the question asks us,
approximately how long does it take Divya to complete one revolution on the Ferris Wheel? All right, so this is
interesting, so this is when she's at the bottom of the Ferris Wheel, so then she gets to the
top of the Ferris Wheel, and then she keeps rotating until she gets back to the bottom of
the Ferris Wheel again. So it took her 60 and t
is in terms of seconds. So it took her 60 seconds
to go from the bottom to the bottom again, and
in another 60 seconds, she would have completed
another revolution. And so let me fill that in, it is going to take her 60 seconds, 60 seconds, and we of course can check
our answer if we like. Let's do another one of these. So here we have, a doctor observes the electrical activity of Finn's heart over a period of time. The electrical activity of
Finn's heart is cyclical, as we hope it would be, and peaks every 0.9 seconds. Which of the following graphs could model the situation if t stands
for time in seconds, and e stands for the electrical activity of Finn's heart in volts? Over here it looks like
we peaked at zero seconds, and then here we're peaking
a little bit more than one, this looks maybe at 1.1,
maybe at 2.2 and 3.3. This looks like it's
peaking a little bit more than every one second, so
like maybe every 1.1 seconds, not every 0.9 seconds, so I'd rule out A. This one is peaking, it
looks like the interval between peaks is less than a second, but it looks like a good
bit less than a second. It looks like maybe every three quarters of a second, or maybe every
four-fifths of a second. Not quite nine-tenths,
nine-tenths this first peak would be a little bit closer to one, but this one is close. Choice C is looking good. The first we're at zero,
then the first peak, this looks pretty close to
one but it's less than one. It looks like a tenth less
than one, so I like choice C. Now choice D, it looks like we're peaking every half-second, so
it's definitely not that. So this looks like a peak
of every 0.9 seconds. This is the best representation that I... This is the best representation
that I can think of. And you can actually verify that. If you have a peak every 0.9 seconds, you're going to have four
peaks in 3.6 seconds. So one, two, three, four, this looks like it's at 3.6. Over here, you have one, two, three, four, you've had four peaks in
less than three seconds. So this one definitely isn't 0.9. So instead of just even forcing yourself to eyeball just between
this peak and that peak, you can say well, if
we're every 0.9 seconds, how long would three
peaks take or four peaks, and then you can actually
get a little bit more precise as you try to eyeball it. So we can check our answer and
verify that we got it right.