 Retarded oscillator driven by a two-sided exponential

ID: retarded-oscillator-driven-by-a-two-sided-exponential

For

g (t) = α e^{- α ∣ t ∣} /2

with

α > 0

Q_{R} (t) = \frac{α}{2 ( 1 + α ^{2} )} {e^{α t}, e^{- α t} + 2 α sin t, t < 0, t \geq 0.

The coordinate and velocity are continuous at zero. At late times the undamped oscillation has amplitude

α^{2} / (1 + α^{2})

; causality fixes the homogeneous solution only after the no-incoming-oscillation condition is specified.

 New to topics? Read the docs here!