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

Figure 9

The functions appearing in the integrand of the convolution integral (10). The “block” 𝑓_inp(𝑡−𝜆) is riding (being moved) to the right on the 𝜆-axes, as time passes. We multiply the present curves in the interval 0<𝜆<𝑡 and, according to (10), take the area under the result, in this interval. When 𝑡<Δ, only the interval (0,𝑡) is relevant to (10). When 𝑡>Δ, only the interval (𝑡−Δ,𝑡) is actually relevant, and because of the decay of ℎ(𝑡), 𝑓_out(𝑡) becomes decaying.