# 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.

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.

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

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.

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;)

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.

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.

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

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).

• yeah, but your $f(t)$ isn't real valued... Commented Feb 16, 2011 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. Commented Feb 16, 2011 at 13:16