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Linearising Graph of Mass and Frequency

  1. Jul 11, 2016 #1
    1. The problem statement, all variables and given/known data
    I did an experiment about the loading of tuning forks. I added blue tac to one of the prongs on a tuning fork and then weighed it. I then measured the different frequencies for each mass and plotted a graph which ended up looking like a exponential decay graph. The results are shown below :

    Mass(kg): Frequency(Hz):
    0.05179 307.83
    0.05219 305
    0.05269 302.83
    0.05335 301.17
    0.05378 299.83
    0.05572 299.17

    2. Relevant equations
    ω = 2πf
    ω = √(k/m)

    3. The attempt at a solution
    When a tuning fork oscillates it is under SHM as when the prongs oscillate there is a restoring force towards the equilibrium. Using the equations of SHM, I did :
    2πf = √(k/m)
    ∴ f = √(k/m) x 1/2π.

    As, k and π are constants, we can rearrange the equation so that f = √k/2π x √1/m.
    So if I plot f on the y-axis, and √1/m on the x-axis, I should get a straight line with √k/2π, being the gradient. However, I still get a exponential decay looking curve when I try to do that! I've then gone on to try the usual logging both sides and then plotting a graph of lg(frequency) and lg(mass) but I still get a curve which is extremely strange? I tried plotting frequency to (1/mass)². But still I get a curve? Could anybody please point out where I have gone wrong or done something careless? I can't seem to spot the problem and can't linearise the curve!!

    Thank you so much in advance, your help and advice is greatly appreciated!
     
  2. jcsd
  3. Jul 11, 2016 #2

    BvU

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    Science Advisor
    Homework Helper
    Gold Member

    Hello Tikiboom, :welcome:

    For your m you seem to take the mass of the entire fork. But not the entire fork vibrates ! So you want to work around your formula in such a way that you can plot your observation versus m. That way you can estimate m0, the mass that doen's vibrate.

    One other remark: why attach a weight to one prong only ? What frequency do you expect for the other prong ? How does that influence your measurement ?
     
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