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Harmonic Oscilator

  1. May 31, 2014 #1
    1. The problem statement, all variables and given/known data
    A test was made with a basket and 20 gram weights. they were put in the basket which hang on a spring, the basket was raised and released. the period was measured for a few number of weights in the basket. the results are as follows. the first of every pair is the number of weights and the second is the period in seconds:
    (2, 0.53), (3, 0.60), (4, 0.66), (5, 0.72), (6, 0.77)
    Draw a graph of T2 as a function of the number of weights, n. comes out a straight line.
    What is the spring constant and the weight of the basket.

    2. Relevant equations
    Period: $$T=2\pi\sqrt{\frac{m}{c}}$$

    3. The attempt at a solution
    From the above equation $$T^2=\frac{4\pi^2}{c}\cdot m$$
    The slope $$\frac{4\pi^2}{c}$$ based on the last and first couples:
    ##\frac{4\pi^2}{c}=\frac{0.77-0.53}{(6-2)\cdot 0.02}=3\rightarrow c=13.2##
    The spring constant c should be around 10[N/m]
    The intersection with the T2 axis: i take the first pair:
    ##0.53=3\cdot 0.04+B\rightarrow B=0.41##
    I insert this B into: $$T^2=\frac{4\pi^2}{c}\cdot m$$
    And get:
    ##0.41=3\cdot m_{basket} \rightarrow m_{basket}=0.14##
    It should be around 30 grams
     

    Attached Files:

    Last edited: May 31, 2014
  2. jcsd
  3. May 31, 2014 #2

    rude man

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    Not sure why you did what you did, so:

    Your basic period is as you say, T = 2π√(m/k). (Use k instead of c. c is usually associated with damping).

    But you realize that the basket has some mass also. So what is m actually?

    Can you pick data points to solve for T (and incidentally the basket weight also)?
     
  4. May 31, 2014 #3
    You forgot to square the periods.
     
  5. May 31, 2014 #4

    rude man

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    That part the OP already did.

    The second part of the question was "What is the spring constant and the weight of the basket." The provided data was in T, not T2,
     
  6. May 31, 2014 #5
    No, they didn't. They forgot to do it. Look at their calculation of the slope.
     
  7. May 31, 2014 #6

    rude man

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    You're right, I saw the graph & thought they got it right. I should have read the part where they said they didn't!

    Anyway, my response was to part 2 only.
     
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