anonymous
  • anonymous
Why is kx=25N instead of -kx=25N?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
anonymous
  • anonymous
anonymous
  • anonymous
shouldn't F=-kx?

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anonymous
  • anonymous
anonymous
  • anonymous
Ahh this my physics teacher went over
anonymous
  • anonymous
cool! Now you can explain it to me :)
anonymous
  • anonymous
the negative explains how that force is acting upon the spring
anonymous
  • anonymous
it depends on the what you're trying to find
anonymous
  • anonymous
if you're trying to find the force the spring is exerting on the mass or the mass exerting on the spring
anonymous
  • anonymous
Hmmm let's see|dw:1353379482698:dw|
anonymous
  • anonymous
|dw:1353379572781:dw|
anonymous
  • anonymous
well I guess we're stretching to a certain length, so the first figure?
anonymous
  • anonymous
I mean the first figure you drew
anonymous
  • anonymous
the figures are the same
anonymous
  • anonymous
it depends on whether you're trying to find the length of the spring or the position of the mass
anonymous
  • anonymous
Uhm I think we want my figure because In your figure we have to consider the gravitational force and the restoring force. I don't think they want to consider the gravitational force
anonymous
  • anonymous
if it asked abouthe spring itself it'd be negative
anonymous
  • anonymous
there is two ways this question can be answered 1) How long did the spring stretch from initial 2) What is the position of the mass after initial. They're the same thing
anonymous
  • anonymous
so since it's asking for position of the mass it's this|dw:1353379915405:dw|
anonymous
  • anonymous
why is it positive? because it is going in the direction that we designated as positive?
anonymous
  • anonymous
yes
anonymous
  • anonymous
technically this question can have 2 answers + answer and a - answer depending on how you set up your axis
anonymous
  • anonymous
OH I see! |dw:1353380068540:dw| Like so?
anonymous
  • anonymous
Now I can say that F=kx
anonymous
  • anonymous
right?
anonymous
  • anonymous
no the other way around, I should probably make the restoring force positive...
anonymous
  • anonymous
|dw:1353380229463:dw|
anonymous
  • anonymous
yeah the picture they used was probably a free falling mass
anonymous
  • anonymous
and saying that the sum of the force of gravity + any other force = F
anonymous
  • anonymous
Yeah that makes more sense. so they probably had up as positive and down as negative.
anonymous
  • anonymous
yes but it really just depends on what you define it... if your teacher marks you wrong and your diagram says otherwise just clear it up with him
anonymous
  • anonymous
yep
anonymous
  • anonymous
so why is k(0.2) why 0.2? How did they come up with x=0.2?
anonymous
  • anonymous
never mind
anonymous
  • anonymous
LOL
anonymous
  • anonymous
that's the displacement haha
anonymous
  • anonymous
yes the displacement will still be posive
anonymous
  • anonymous
hmm interesting: (this the DE part of my calc II book) \[2\frac{d^2x}{dt^2}+128x=0 \text{ has the solution }x(t)=c_1cos8t+c_2sin8t \] yeah that's easier that doing it manually....
anonymous
  • anonymous
It's convention to designate potential energy as negative. The reaction force of the spring is opposite the positive applied force.
anonymous
  • anonymous
More clearly: The negative sign of F=-kx means that the spring force is opposite to the applied force on the spring.
anonymous
  • anonymous
potential energy as positive...the restorative force?
anonymous
  • anonymous
Yes that makes sense
anonymous
  • anonymous
I had to reread the last sentence you wrote several times, but it makes sense now
anonymous
  • anonymous
but where did they get the 8 in sin and cos 8t
anonymous
  • anonymous
As others mentioned above, it's a sign convention. You define what direction you want to be positive and anything opposite to that is negative. The norm, though is to treat spring force as negative/opposite to any force acting *on* the spring.
anonymous
  • anonymous
The 8 is based on the period of the spring - that is determined by the spring constant, k, and the attached mass.
anonymous
  • anonymous
\(\large T=2\pi \sqrt{\frac{m}{k}}\) T^-1 is the frequency of oscillation.
anonymous
  • anonymous
yep, sounds good. I googled it LOL \[T=2\pi \sqrt{\frac mk}\]
anonymous
  • anonymous
The "8" in the cosine function usually goes by the name, omega, \(\large \omega\). Might want to look that up too.
anonymous
  • anonymous
so the formula is \[x(t)=c_1cosTt+c_2sinTt\]
anonymous
  • anonymous
so T is \[\omega\]
anonymous
  • anonymous
\(\large . . . cos(\omega t) . . \) No, ω is related to T.
anonymous
  • anonymous
Oh \[\omega=\sqrt{\frac km}\]
anonymous
  • anonymous
Right!
anonymous
  • anonymous
\[x(t)=c_1cos\omega t+c_2sin\omega t\]
anonymous
  • anonymous
Yes, you can either derive that using the Diff.Eq. or look it up on a physics formula sheet. (Depends on if you are more mathematician or engineer ;-) )
anonymous
  • anonymous
leaning more towards engineering....physics formula sheet :P
anonymous
  • anonymous
omega doesn't seem to have units
anonymous
  • anonymous
That would be my choice too, but know that the way the physicists got those formulas in the first place was to solve the DEs (or rather to get their math dept. grad students and TAs to do the solving for them..)
anonymous
  • anonymous
omega should have units of s^-1, it's a frequency.
anonymous
  • anonymous
Or .. is at least based on a frequency, something in the derivation might make the units cancel, but I'm pretty sure it's just the reciprocal of the time period, T.
anonymous
  • anonymous
radians per second
anonymous
  • anonymous
according to my friend wiki
anonymous
  • anonymous
so s^-1 should be sufficient, i can leave the radians part out in my notation?
anonymous
  • anonymous
Yes, because radians are dimensionless (it's derived from length ÷ length), that's what the 2π conversion factor is in there for.
anonymous
  • anonymous
Oh I see
anonymous
  • anonymous
why is c_2 zero? shouldn't it be ...so when we say\[ x(0)=8c_2 cos8t\] does that mean \[0=8c_2 cos8t=8c_2cos(0)=8c_2(1)=c_2\] yep that seems right LOL
anonymous
  • anonymous
Thanks everyone!!!!

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