Question

Need help finding an equation relating period and length. Will medal.

Answer 1

Ill write out what the question is asking:

Data for the period of a pendulum as a function of its length:
HINT: Try graphing period vs. length^(1/2)

Period(s): 1, 1.4, 1.75, 2, 2.5, 2.85
Length(m): 0.25, 0.5, 0.75, 1, 1.5, 2

Answer 2

So, I graphed the "Hint" and got values of:

Period(s): 1, 1.4, 1.75, 2, 2.5, 2.85
(length)^(1/2): .5, .707, .866, .1, 1.22, 1.41

with m= .49 and b= .02

Answer 3

Depending on what you had on your x axis you have:
$$y = mx + b$$
now it could be that
$$t = 0.49\sqrt L + 0.02$$
that's an equation. Not sure if it's the one you're looking for.

Answer 4

I got that equation, I'm having trouble finding an equation for the original data set. We are supposed to use the equation second data set to find an equation for the first, if that makes sense.

Answer 5

Not sure you only posted the one data sample. What happens when you use the same formula on the second data set? Does it not fit? Why? For what m does the 2nd data set fit?

If everything fails make sure you did the fit right. I don't think you did because the pendulum equation is:
$$t = 2\pi \sqrt \frac{L}{g}\\
t = 2\pi \frac{\sqrt{L}}{\sqrt{g}}\\
t = \frac{2*3.314}{\sqrt{9.81}}\sqrt{L}\\
t = \frac{2*3.14}{3.13}\sqrt{L}$$
which is approximately
$$t=2\sqrt{L}$$
and not
$$t=0,5\sqrt{L}$$
which is what you approximately got