I'm reading through Kleppner and Kolenkow's Introduction to Mechanics (2nd ed), and in it, they go through the example of an electron subject to an oscillating electric field (example 1.11). The example and the math is straightforward, but at the end of the explanation, they say:
Here is the problem statement:
The ionosphere is a region of electrically neutral gas, composed of positively charged ions and negatively charged electrons, that surrounds the Earth at a height of approximately 200 km (120 mi). If a radio wave passes through the ionosphere, its electric ﬁeld accelerates the charged particles. Because the electric ﬁeld oscillates in time, the charged particles tend to jiggle back and forth. The problem is to ﬁnd the motion of an electron of charge−e and mass m which is initially at rest, and which is suddenly subjected to an electric ﬁeld E = $E_0$ sinωt (ω is the frequency of oscillation in radians/second).
And the evaluation portion (the italicized one) writes:
RESULT: The electron is initially at rest, $x_0$ = $v_0$ = 0, so we have x(t) = ($a_0$/ω) t − ($a_0$/$ω^2$) (sinωt).
The result is interesting: the second term oscillates and corresponds to the jiggling motion of the electron that we predicted. The ﬁrst term, however, corresponds to motion with uniform velocity, so in addition to the jiggling motion the electron starts to drift away. Can you see why?
I'm not sure I'm able to see why, as they say. I understand that the drift comes as a result of the integration step. If you double integrate a sine, you have a constant term that then becomes the drift term, but I'm not seeing an "aha" explanation as they seem to suggest. I feel like I'm missing an insight that they are referring to. Am I?