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Oscillation in spring mass system questions

  1. Feb 3, 2014 #1
    1. The problem statement, all variables and given/known data

    I am having an issue with answering number 4 in the attached image.

    2. Relevant equations

    Relevant equations are given in question 3.

    3. The attempt at a solution

    Squaring the equation would only make it easier to solve for any of the other variables, or the period squared. I cannot see the correlation with the square of the period. Would it just make it more accurate?
     

    Attached Files:

  2. jcsd
  3. Feb 4, 2014 #2
    It's an oddly worded question -- I think the only thing it's getting at is that, like you said, it would allow you to solve for m or k, and it would also allow you to see the relationships of the variables more clearly.

    With the original equation you have:
    [itex]T = 2\pi\sqrt{\frac{m}{k}}[/itex]

    So that means [itex]T \propto \sqrt{\frac{1}{k}}[/itex], so graphing [itex]T[/itex] vs. [itex]\sqrt{\frac{1}{k}}[/itex] would give you a linear relationship, and you could solve for k.

    If you square both sides, you get:
    [itex]T^{2} = \frac{4\pi^{2}m}{k}[/itex], so [itex]T^{2} \propto \frac{1}{k}[/itex], so graphing [itex]T^{2}[/itex] vs. [itex]\frac{1}{k}[/itex] would also give you a linear relationship, and you could solve for k that way too. So maybe that would be little easier? It really just depends on what data you have.
     
  4. Feb 4, 2014 #3

    I see where you are coming from! just makes no sense to me to square it given I had all the variables in the experiment that we did in class. Maybe for future reference know this is something great to remember. Thanks Jack!
     
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