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Homework Help: SHM mass and spring constant with given frequency

  1. Mar 2, 2010 #1
    1. The problem statement, all variables and given/known data

    With a block of mass m, the frequency of a block-spring system is 1.5Hz. When 80g is added, the frequency drops to 0.9Hz. Find m and the spring constant k.


    2. Relevant equations

    T=1/f
    w=2pi/T
    so w= 2pi*f
    w^2=k/m
    so k=mw^2
    T=2pi*sqrt(m/k)

    3. The attempt at a solution

    The problem seems simple enough. I just have to set up 2 equations to solve one unknown and then find the other right?
    So first i found the w for when the mass= m and f= 1.5Hz (i called this w) and the w for when mass= m+0.08 and f= 0.9Hz (W).

    Using the formula w= 2pi*f, i found 9.42 for w and 5.65 for W.

    Then I set up the 2 equations:

    k = mw^2 = 88.8m
    and
    k = (m+0.08)W^2 = 31.9m + 2.55

    After i did equation 1 = equation 2, so:
    88.8m = 31.9m + 2.55 and this gave me m=22.3

    But the correct answer for m is supposed to be 0.045 kg. Can somebody let me know what I'm doing wrong please?

    The correct value for k is supposed to be 3.99N/m
     
  2. jcsd
  3. Mar 2, 2010 #2

    collinsmark

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    Homework Helper
    Gold Member

    Try redoing the above step again. I think that's where the trouble is coming from.
     
  4. Mar 2, 2010 #3
    I'm not exactly sure which steps you're asking me to redo but i'll show my calculations in more detail if that's what you meant.

    w= 2pi*f1 = 2pi*1.5 = 9.42 rad/s
    W= 2pi*f2 = 2pi*0.9 = 5.65 rad/s

    Then,

    1) k= mw^2 = m*9.42^2 = 88.8m
    2) k= W^2(m+0.08) = 5.65^2(m+0.08) = 31.9m + 2.55

    I really still don't see what's wrong with the way I'm doing it..
     
  5. Mar 2, 2010 #4

    collinsmark

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    Homework Helper
    Gold Member

    So far so good. It's the next step where you solve for m (after you set the equations equal).
     
  6. Mar 2, 2010 #5
    Well ok..

    Equation 1 = Equation 2

    88.8m = 31.9m + 2.55

    then bring the "m" terms to one side

    88.8m - 31.9m = 2.55

    56.6m = 2.55

    and then divide..

    Ahhh!! wow i feel really stupid.. i was dividing both sides by 2.55 all this time.. I get it now, thanks a lot
     
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