1. The problem statement, all variables and given/known data

Hello everyone,

I'm in need of some assistance in regards to deriving an equation from a graph. I have been tasked to graph information which I've collected through experimentation and then write an equation to represent the graph.

I'm stuck at steps 3 and 4 and I am not really sure on how to approach the questions. I know that I have a power graph and if I square the frequencies that I obtained I come to a linear graph.

Here is a direct link to the graphs that I've made:

Firstly, you only need to derive an equation from linear graph (the one with the straight line), not the curved one. So looking at you graph, you have a (roughly :s) straight line when you plot F_{c} vs. f^{2} and therefore you can say that that F_{c}[itex]\propto[/itex]f^{2}. Now, you should be able to write an expression with a constant of proportionality, and what is the general expression for a straight line...?

Well the general expression for a straight line is Ax + By + C = 0, or y = mx + b.

I know it's a very rough linear graph but my teacher only wants the use of whole numbers such as 2 or 3 rather than decimals as exponents. So from here how would I write the proportionality statement of Fc[itex]\propto[/itex]f^2 using the equation of the linear graph?

Fc[itex]\propto[/itex]f^2 if I remember correctly, becomes an equation such as [itex]Fc = Kf^2[/itex] where K is a constant. Is this true?

P.S. I'm new to the latex system so please bare with me ...

y is the same as f (x) where f is centripetal force, and x represents frequency. So could I then say that Fc(frequency) = mx + b ? or am I missing something here?

Looks good to me . Depending on your data you may have to add in a constant (which would be the y axis intercept + C), but this constant would be due to the standard error of your data. And yes k would represent the gradient of the line, if you have a proper line fitting program I would use that, but failing that excel does a reasonable job of plotting lines of bet fit.

Then my guess would be the line of best fit drawn by excel would be sufficient for High School level, but it might be worth checking with your teacher.