1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Plotting Straight Line Graphs

  1. Jun 15, 2013 #1
    So, I have to assess the relationship between the Constant of a Spring and the Time Period of Oscillations.

    I have researched the equation that links the two and I know that to have a straight line graph I need to plot:

    T2 against 1/K

    However, I do not know why; how I get to that conclusion.

    I have read about log-log graphs and played around with the concept to see if it would yield the plot I mentioned above. I tried plotting for the log of T against the log of K and I did get a straight line plot. I checked if my gradient was equal to -0.5 and my y-intercept was equal to (log 2∏-0.5 log m) and they were, but I still do not understand why I have to plot T2 against 1/K.

    Can anyone please shed some light onto this please?

    Thanks in advance!
  2. jcsd
  3. Jun 15, 2013 #2


    User Avatar
    Homework Helper

    You are asked to plot that because of the derivation of the periodic time formula for a spring oscillation.

    The final equation is

    [tex]T = 2 \pi \sqrt{\frac{m}{k}}[/tex]

    If you square both sides you will get

    [tex]T^2 = \frac{4 \pi ^2 m}{k}[/tex]

    Which is the form Y=MX where Y = T2 and X = 1/k.

    Thus plotting Y vs X i.e. T2 vs. 1/k will give you a straight line. So you can get the mass oscillating if you desire from the gradient of the graph you plotted.
  4. Jun 15, 2013 #3
    I like your idea of using a log-log plot much better. I have over 40 years of experience as a practicing engineer, and that is the way I would do it. Congratulations on thinking out of the box.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted