SHM mass and spring constant with given frequency

  • Thread starter k77i
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Homework Statement



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.


Homework Equations



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

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
 

Answers and Replies

  • #2
collinsmark
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88.8m = 31.9m + 2.55 and this gave me m=22.3

Try redoing the above step again. I think that's where the trouble is coming from.
 
  • #3
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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..
 
  • #4
collinsmark
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Gold Member
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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..

So far so good. It's the next step where you solve for m (after you set the equations equal).
 
  • #5
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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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