One More Tool for Understanding Resonance and the Way for a New Definition

Figure 11

The simplified ℎ(𝑡) (named ℎ_𝑆(𝑡)): there is no damping at 0<𝑡<1/𝛾, but for 𝑡>1/𝛾, it is identically zero, that is, we first ignore the damping of the real ℎ(𝑡) and then cut it completely. This idealization expresses the undoubted fact that the interval 0<𝑡<1/𝛾 is dominant and makes the treatment simpler. A small change in 1/𝛾 which makes the oscillatory part more pleasing by including in it just the (closest) integer number of the half waves, as shown here, may be allowed, and when using ℎ_𝑆(𝑡) in the following we shall assume for simplicity that the situation is such.