Continuing:
Electromechanical systems are very interesting, but I will refer you to textbooks for detailed understanding.
Strictly mechanical systems, such as a car suspension, have a primary resonant frequency from the mass m and the spring constant k: w0 = (k/m)1/2.
To damp that, the shock absorber exerts a force that opposes the velocity to provide mechanical resistance.
Note that damping requires a force proportional to velocity, not a frictional force independent of velocity.
In the shock absorber, this results from a viscous liquid being pushed through small apertures: another term is "dash pot".
For the MM cartridge, the interaction between the (fixed) coil and the moving magnet gives a voltage source (proportional to the magnet velocity), and the current through the coil applies a proportional force to the moving assembly.
The voltage induces a current in the total electrical circuit, which includes the electrical inductance of the coil, its electrical resistance, and the external impedance of the amplifier.
Now, mechanically, the variables are velocity and force: force times velocity is power.
Electrically, the variables are voltage and current: voltage times current is also power.
You can convert the mechanical part of the system into an equivalent electrical circuit, replacing force and velocity with current and voltage, and the parameters mass and compliance (inverse of spring constant) with equivalent capacitance and inductance (I forget which order), add the electrical components, and you get two coupled resonant circuits that transform the needle velocity to the amplifier input.