How can we describe the vibrational motions of a molecule? We can think about a diatomic molecule (Figure 6.3.1) as two atoms with masses, and a chemical bond between them as a spring. This is not a perfect analogy, because a spring and two masses at the macroscopic level do not behave in exactly the same way that two atoms connected to each other through chemical bonding will act at the quantum level. But, this analogy is a convenient place to start!

**Figure 6.3.1.** A model visualizing molecular vibrations. Two atoms are connected by a spring to account for the flexibility of the bond. (Tby11, Creative Commons CC0 1.0 Universal Public Domain).

**Learning Objectives**

- Describe the motion of a spring.
- Relate the spring constant to the stiffness of a spring.
- Relate the motion of a spring to the frequency or energy of a simple harmonic oscillator.

**Prior Knowledge and Skills**

3.5 The Dual Nature of Electromagnetic Energy

3.7 Electromagnetic Energy: Units Conversion

6.2 Chemical Bonds Vibrate

**Key Terms**

- Spring Constant
- Hooke’s Law
- Simple Harmonic Motion

**Guided Inquiry**

Watch parts of this video: 8.01x – Lect 10 – Hooke’s Law, Springs, Pendulums, Simple Harmonic Motionhttps://youtu.be/tNpuTx7UQbw

From 0:00 to about 4:20 (Spring constant and Hooke’s Law)

From 8:57 to 11:00 (The connection between simple harmonic motion of a spring and the wave frequency/energy as opposed to amplitude)

Hook’s Law is:

[Equation 6.3.1] F = – k x

**6.3.1.** What is k in this equation?

**6.3.2.** Compare a stiff spring to a weak spring. Which one would have the higher k, and why? Hint: solve for x in equation 6.3.1 and think about how a higher k would affect the force needed to move the spring the same distance.

Here is the potential energy curve for a spring. As you saw in the video, the spring moves back and forth, or oscillates, in a sinusoidal fashion. This is called a **simple harmonic oscillator.**

Interact with a potential energy diagram to see how the potential energy diagram above was created!

Go to this PhET interactive diagram on Hooke’s Law: https://phet.colorado.edu/sims/html/hookes-law/latest/hookes-law_en.html

Choose “Energy” (the third option). Once you are there, choose “Energy Plot” on the right menu. Grab the spring with the claw and move it back and forth!

**6.3.3.** When does a spring have its lowest potential energy?

**References**

Elastic potential energy: http://hyperphysics.phy-astr.gsu.edu/hbase/pespr.html