[aferdita]

The vibrational energy spacings for the hydrogen halides are :
HF: 3958.4 cm-1
H35Cl: 2885.6 cm-1
HBr: 2559.3 cm-1
HI: 2230.3 cm-1
Calculate the force constants. Do you notice any trends in the force constants? Suggest an
explanation for the trend or the lack of a trend.

so F=-kx but since there is no displacement, is there some other equation
x(t) = x_o sin(omega"t) with " omega=square root(k/m)= 2Piv
is this the equation to use, were omega is the frequency.

[Yggdrasil]

From a quantum mechanical treatment of the harmonic oscillator, you can derive the vibrational energy levels which will give you the vibrational energy spacings in terms of Planck's Constant and the natural frequency of the vibration.  For diatomic molecules, the natural frequency is related to the force constant of the bond and the reduced mass of the two molecules.  The following wikipedia article has most of the information you'll need:

http://en.wikipedia.org/wiki/Quantum_harmonic_oscillator