# Example of a time varying function which can be easily measured

My sister is in 10th grade. She doesn't seem to understand the concept of time varying functions (current, light, sound wave forms etc). I explained her in easiest possible terms. She got it but not very comfortable with the concepts.

So, instead of explaining. I simply wanted her to take a stopwatch & measure "something" and tabulate all the values. Then plot them on a graph paper.

Now I'm thinking of that "something" that she can measure. I want something that has following properties:

1. It must vary every second or two. (because it would be more intuitive than something that varies after a while).
2. Its variation should be function of some known function like. Periodic function like Sine or Cosine would be great but any known function would do.
3. Please see the tag "home-experiment". I mean that :)

I cannot think of any such thing. I thought may be you could help.

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Just a piece of advice. Don't use something too concrete; kids learn better when there is some kind of abstraction in the lesson because in this way, they can apply the learned principles to other situations. Of course, you can reinforce it with examples. – Robert Smith Feb 14 '11 at 17:36
I changed your title to make it clearer. If you don't think the change is helpful let me know and I can roll it back. – user346 Feb 14 '11 at 18:24

I always get the kids with some sporty things. I would suggest to measure hers or yours time dependent position while sprinting. This is very handy and you can explain to her a lot of physical concepts coming from mechanics like velocity, acceleration, total distance, ... and also some measurement/error things. I found a nice picture illustrating the idea:

Greets

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+1 Well, that's a great idea. We both can sit on a bike & note down the time & speed of the bike. Wouldn't that be ideal? I can increase & decrease speeds sinusoidally too. – claws Feb 16 '11 at 11:05
@claws: Thank you. As you said, you can play around with the idea a little and come up with something that suits best to your sister - like a record on bike rides, swimming speeds, number of jumps per ten seconds... The only importance is that your sister actually likes the action. If this is the case she will be very keen on learning new things from you :) Greets – Robert Filter Feb 16 '11 at 13:54

Height of water accumulated in a bucket from a constant supply source. If the bucket is cylindrical height will be a linear function of time. If it is conical it will be a parabolic function etc.

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+1 that's a good idea. – claws Feb 14 '11 at 17:54
+1 On a similar note, evaporation of water from an open bottle. I like this better because it also connects with atomic hypothesis and you have plenty of time to measure it while at the same time you don't have to wait too long (which is a problem with e.g. height measurements). – Marek Feb 14 '11 at 23:03

For a slower function, try the angle of the sun over the course of a day. To measure, just put a stick in the ground and look at the shadow. Also a great way to introduce some trig as well as the effect of amplitude vs season.

For some of the faster suggestions here like pendulums, try recording it with a video camera if you have one. The recording function on most hand held cameras should be fine, and then you can step through the video a few frames at a time to measure your function.

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use an analog clock and measure the angle traveled by the minute hand (or the second which is faster but is less time to take notes) over time. It is cyclical and can introduce the functions sine, cosine,.. and uses the same clock for measuring the elapsed time;)

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+1. Godd idea. Thanks for a periodic time function. :) – claws Feb 16 '11 at 5:51

Set up a simple pendulum with a string and a heavy object--a barbell will do. You can hang it from a tree branch if you need space to do it. The period varies as $T=2\pi\sqrt{\frac{L}{g}}$, where $L$ is the length of the pendulum, and $g$ is the local acceleration due to gravity, roughly $32 {\rm \frac{ft}{s}}$. It shouldn't be too hard to adjust the length of your pendulum so that the period is something sensible and easily measurable--a ten foot pendulum should have a period of about 4 s, so it should be possible to measure position versus time for a variety of positions along the weight's path.

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Jerry, its sqrt( L/g ) ! And 1 meter is T = 2 s – Georg Feb 14 '11 at 17:44
Fixed. Ah, typos. I don't get your objection about one meter, when I was giving values in feet. – Jerry Schirmer Feb 14 '11 at 17:48
Jerry its just my aid of memeory, because 1 m pendulums are common in old clocks. (But clockmakers name that a "one second" pendulum, because in one swing, the clock mechanism counts 2 teeths of a cam wheel.) So for 10 ft = 3 meters I would calculate 2 s times sqrt(3) about 3.5 s. Another approximation is (since sqrt(g) about Pi) is T =2 squrt(L) in meters – Georg Feb 14 '11 at 18:16

Width of chest while breathing. Height while growing. loudness of heart sounds in a stethescope. Distance while walking (try walking in circles as well). Physiology makes it personal.

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Something like the raise in temperature of water that you use for cooking. Very home-experiment-like.

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Not so easy to measure & its function is not something known. – claws Feb 14 '11 at 17:55
@claws: put a thermometer in boiling water. I would expect that the function would be linear if the pot is stirred well enough. – Jerry Schirmer Feb 14 '11 at 18:39
Watch out not to use a medical thermometer; it will break. Maybe an oven thermometer. Or could use a different temperature range, e.g. from 100 deg. F to room temp., i.e. letting it cool in different shaped vessels – sigoldberg1 Feb 14 '11 at 20:31

I wouldn't use abstract concepts or things that are too related to physics.

Try with f(t) = "which program is on air on a given TV channel".

It is time-varying, it is easily measurable AND it is something she will likely be acquainted with. And it has some periodicity inside (like news, it is always at the same hour).

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yeah, but your $f(t)$ isn't real valued... – Tobias Kienzler Feb 16 '11 at 12:45
The OP didn't impose such a constraint. Yes he wants to plot the values, but this can be obtained by assigning a real value to each TV program. – Andrea Spadaccini Feb 16 '11 at 13:16