Читать книгу Vibroacoustic Simulation - Alexander Peiffer - Страница 17

Here, the roots are complex conjugates and the solution of Equation (1.10) becomes:

(1.13)

(1.14)

The motion is oscillatory with a frequency that is lower than in the undamped configuration:

(1.15)

Introducing the initial conditions u₀ and vx0 at t = 0 the solution for the initial amplitude u^0 and phase ϕ₀ reads as:

(1.16)

(1.17)

The damped oscillatory motion is illustrated in Figure 1.3. It shows a decreasing motion that never approaches the equilibrium.

Figure 1.3 Damped, sinusoidal motion of the underdamped oscillator. Source: Alexander Peiffer.