Easily measurable non-linear physical relationships.

[Vindicta]

I've been trying to think of a really good experiment in which the data gathered would be non-linear. The only ideas I've managed to come up with were either way to simple and boring, or way to hard for me to set up and measure accurately. Some examples of experiments include splash radius of a water balloon vs. height of the drop, number of Mentos in pop vs. height of eruption, consumption of fuel vs. velocity of vehicle, and degree of curve/deviation vs. magnitude of spin on a ball in a fluid. These are just some of my ideas. The first two being rather simple, and the latter two being a bit too difficult.

Anyways, I was wondering if any of you have a cool experiment idea for me. Even if someone could list some non-linear physical relationships that might inspire me to design an experiment around it, it would be very appreciated.

Thank you!

 

[Studiot]

The pitch of a violin string is proportional to the square root of the tension ans inversely proportional to the square root of the density, so you could investigate vibrating strings.

$$pitch(f) \propto \frac{1}{l}\sqrt {\frac{T}{\rho }}$$

 

[Vindicta]

That's a great idea! Something I could definitely attempt. Any suggestions on how I could measure the high amount of tension accurately with limited tools? I was thinking just a Newton spring scale, but I have a feeling a violin string would max the scale out.