# Spring Mass Damp - Differential Eq

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.

• "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. – Did Nov 8 '14 at 22:55
• but the equation is incomplete. – KevinCameron1337 Nov 8 '14 at 22:56