How would one take the Fourier Transform of $$ m\frac{d^2x}{dt^2}+m\omega_0^2 x + m\Gamma \frac{dx}{dx} = -eE $$ to get $$ -m\omega^2 x+m\omega_0^2 x + jm\omega\Gamma x = -eE $$

This is in our class lecture notes for nanophotonics, specifically relating to the Lorentz model in plasmonics, but I am having trouble understanding how our professor got from the first expression to the second one.

How would one take the Fourier Transform of $$ m\frac{d^2x}{dt^2}+m\omega_0^2 x + m\Gamma \frac{dx}{dt} = -eE $$ to get $$ -m\omega^2 x+m\omega_0^2 x + jm\omega\Gamma x = -eE $$

This is in our class lecture notes for nanophotonics, specifically relating to the Lorentz model in plasmonics, but I am having trouble understanding how our professor got from the first expression to the second one.

How would one take the Fourier Transform of:

To get:

This is in our class lecture notes for nanophotonics, specifically relating to the Lorentz model in plasmonics, but I am having trouble understanding how our professor got from the first expression to the second one.

I appreciate your feedback.

How would one take the Fourier Transform of $$ m\frac{d^2x}{dt^2}+m\omega_0^2 x + m\Gamma \frac{dx}{dx} = -eE $$ to get $$ -m\omega^2 x+m\omega_0^2 x + jm\omega\Gamma x = -eE $$

This is in our class lecture notes for nanophotonics, specifically relating to the Lorentz model in plasmonics, but I am having trouble understanding how our professor got from the first expression to the second one.