The mass-spring system is a useful model to help you gain insight into the vibrational behavior of chemical bonds and of vibrations along lines of intermolecular force. In other words, there is a fruitful interdisciplinary connection between the simple mechanics of harmonic motion and some important topics in chemistry.
The C-H stretch vibration in ethane is at a lower frequency than in ethylene, where the greater s character leads to a somewhat stronger bond.
Chemical behaior is rarely a pure reflection of the bare-bones model system from physics, but the basic physics is often an excellent starting point, so, although the relationship between force and separation is very different and, is, in fact, the chemical bond is a quantum-electrodynamic system, not encompassed by classical mechanics, let us consider a covalent bond an effective spring for a moment to help us understand certain aspects of its behavior.
Molecules vibrate and acquire vibrational energy. The relationships between electrostatic force, particle mass, and frequency (which produces a frequency of emitted radiation (infrared, microwave, etc.)) are similar to the relationships between spring constant, object mass, and frequency of spring oscillation. Larger masses and weaker forces give lower frequencies.
In organic chemistry, think about this the next time you look at the stretch vibrations in an IR spectrograph. Similarly to a weak spring connected to a large mass, thhrough their stretch vibrations, large atoms combined by weak bonds absorb lower energy (lower frequency) infrared photons than small atoms combined by strong, rigid bonds.
Although Hooke's Law most definitely does not provide a complete description of the force vs. distance relationship of a covalent bond, it provides a relatively good model for small amplitude vibrations, and it can be fruitful to think of covalent bonds as springs to relate bond strength and the masses of bonded atoms to stretch frequency.
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