the LHS isn't energy, but rate of change of it. If there is no driving term, eventually all the energy gets lost - and the thing comes to rest. Then as energy is changing no longer, the LHS is also zero. At this pint you can see that the rhs is also zero. Theoretically, this happens after...
This is where you went wrong. The energy here is not conserved within the system, so you can't put the rate of change to zero. The SHM is a closed system, this is not. Here the energy keeps changing, the external force F(t) is pumping in energy while the damping is siphoning it out. Your...
Franz, I did not mean that the derivation does not require the field strength. What I meant was the formula for the ratio of the two components.
Suppose we have an arbitrary vector v along a particular direction ( making theta with x-axis, say) Then the ratio : \ v_y / \v_ x = \ tan \theta...
All that was used in the derivation was that the fact that the electric field is directed along the 'kink' that was drawn. Field lines describe the direction of the electric field, and the derivation of the formula you mention only needed that direction. Nothing about the strength (magnitude )...