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Homework Help: Lab Problems with Simple Harmonic Motion in Springs

  1. Dec 4, 2011 #1
    1. The problem statement, all variables and given/known data
    During lab we measured the amount a spring was stretched when various masses where hung on it to verify Hooke's Law. We started with a 50 gram mass and then increased with 50 grams up until 350, for seven measurements. We then graphed the force and displacement. The lab manual says that the slope is k, the spring constant ( with force on the y axis and displacement on the x-axis).
    When we did this we only got a slope of 0.1 meter.

    We were then asked to find the period of oscillation. We used a stopwatch to time 20 oscillations for three different masses. Then we used the equation T=2∏√M/k
    T is the time for the period, M is the mass and k is the spring constant
    However our numbers were no where near the actual value. They didn't even make since. Obviously it doesn't take 7 seconds to oscillate. The final step was to determine the effective mass of the spring and to consider that in the calculation for the oscillation time as well, which only made our numbers even more off. What could have went wrong.

    2. Relevant equations
    T is the time for the period, M is the mass and k is the spring constant

    3. The attempt at a solution
    The measured time for osculation with a 50 gram weight attached was 0.7155 seconds. That is approximately what I get when I take √M/k, before multiplying by 2∏.

    The measured time with 150 g was 0.95s. When I used the equation I got 7.7s.

    The only thing I can think of is that the k is wrong. Everything else are constant numbers. I substituted 0.7155s into the equation and came up with k=3.855, but I have been back over my numbers in the first section and cannot see where something when wrong there.

    The initial, resting length of the spring was 28.2 cm. With each trial a 50 gram weight was added. Displacement in meters were 0.043; 0.091; 0.144; 0.196; 0.249; 0.297; and 0.348.

    We asked the graduated assistant that teaches our lab, but he said he did not know what we did and was really rude to us (like always). He said our graph looked good so he didn't know. Our final is Tuesday and I still have to write the lab report for this lab. Please, help me out if you know what we did wrong.

  2. jcsd
  3. Dec 4, 2011 #2
    I calculate a different value for the slope.
    Have you remembered to
    -make sure the mass is in kg
    -multiply mass by g to calculate the force?

    The value of k must be in units of Nm-1
    Your answer being out by a factor of about 10 is the clue.
    Last edited: Dec 4, 2011
  4. Dec 4, 2011 #3
    I thought this is what I did as far as the first part. For example, I had 0.50kg * 9.8m/s2= 0.49N.

    I am not sure that I understand the second part where k needs to be in Nm-1. Can you explain that to me?
  5. Dec 4, 2011 #4
    50 gram is 0.05kg not 0.5 kg

    There is the factor of 10 you have lost in the calculation of the slope.

    The slope, k, is force divided by extension. This is Newton divided by meter
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