Click here to purchase the entire book in PDF format. Damping Let's look at that system I just described. We'll put a weight hung on a spring as is shown in Figure 3.2 Figure 3.2: A mass supported by a spring. If there was no such thing as air friction, and if the spring was perfect, then, if you started the mass bobbing up and down, then it would continue doing that forever. Since, as we saw in the previous section, that this is a simple harmonic oscillator, if we graph its vertical displacement over time, then we get a perfect sinusoidal waveform as shown in Figure 3.3 Figure 3.3: The vertical displacement of the mass versus time if there is no loss of energy due to friction. Notice that the frequency and amplitude of the oscillation never change. The mass will bob up and down exactly the same, forever. In real life, however, there is friction. The mass pushes through the air and loses energy on each bob up and down. Eventually, it loses so much energy that it stops moving. An example of this behaviour is shown in Figure 3.4 Figure 3.4: The vertical displacement of the mass versus time if there is loss of energy due to friction. Notice that the fundamental frequency of the oscillation never changes, but that the amplitude decays over time. Eventually, the mass will bob up and down so little that it can be considered to be stopped. There is a technical term that describes the difference between these two situations. The system with friction, shown in Figure 3.4 is called a damped oscillator. Since the oscillator is damped, then it loses energy over time. The higher the damping, the faster it loses energy. For example, if the same mass and spring were put in water, the system would be more highly damped than if it were in air. If they're put in oil, the system is more highly damped than it is in water. Since a system with friction is said to be damped, then the system without friction is therefore called an undamped oscillator.