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The molecular bond due to intermolecular forces is flexible. A diatomic molecule like oxygen ($O_2$), if disturbed, will oscillate to and fro the equilibrium position ( $R_0$ or $x = 0$ minimum potential energy) approximated by the equation: $$ U\ddot{x} + k*x = 0 $$ V(R) - Potential Energy $$ V(R) = 1/2k (R - R_0)^2 = \frac{1}{2}kx^2 $$ the U for ($O_2$) is $1.33 \times 10^{-26}$ and $k=1195$

  1. What is the Natural Frequency of $O_2$
  2. What will happen to the molecule if it is forced by an external source to vibrate with a freq equal to its natural freq?

Hello Community, I am a Software major thats taking a class in DE... something about the wording of this question is giving me problems. I typically dont find Spring/mass questions very hard, but i just cannot figure out what im missing here:

I calculated that : $$ w = 2.999749\times 10^{14} $$ and $$ x(t) = A \cos(w t) + B \sin (w t) $$ but i cannot figure out what the initial conditions would be so i can solve for A and B.

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  • $\begingroup$ "i cannot figure out what the initial conditions would be so i can solve for A and B." You are not requested to solve for A and B. $\endgroup$ – Did Nov 8 '14 at 22:55
  • $\begingroup$ but the equation is incomplete. $\endgroup$ – KevinCameron1337 Nov 8 '14 at 22:56

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