What is the "spring" and what is the "mass" in a loudspeaker system? I've been reading about how speakers work and keep seeing that it is analogous to the mass on a spring system.
I'm trying to identify what is the "mass" and what is the "spring" in the case of the speaker. I think the speaker cone is the "spring" as it is what provides the restoring for when the speaker cone moves.
I'm not quite sure what the "mass" would be though. In the mass-spring system, the mass is something that provides a force that acts to stretch the string. In the speaker system, to me that role seems to be played by the current in the coil and the Lorentz force that makes the speaker cone move.
I have seen other people say that the "mass" is just the mass of the speaker cone. SO perhaps I'm overthinking it.
 A: I will slightly enlarge upon these answers as follows.
Since the cone is well-coupled to the air surrounding it, its effective mass includes the mass of some of that air. A speaker cone operated in a vacuum will not have any air mass coupled to it and will exhibit a slightly higher natural frequency that it has in air.
If we mount the speaker in a sealed box, then as the cone is moved back and forth it will alternately compress and expand the air inside the box. This effect will add the stiffness of the springy air inside the box to the stiffness of the cone's circumferential suspension and similarly raise the cone's natural frequency.
Note also that it is common in speaker design to use a ribbed cone which has circular ridges pressed into it all over its surface. When driven at low frequencies, the entire cone pumps back and forth as a single unit, but as the driving frequency is raised, the outermost annular portions of the cone become decoupled from the inner portions and instead of having a 15" loudspeaker cone, the effective cone diameter is now 12" and its mass is reduced, improving its ability to reproduce high frequencies. Run the frequency up some more and you'll get a 10", then an 8", then a 6" cone.
It is also common to build a cone with an extremely soft, "flabby" suspension and rely on the springiness of the air inside the speaker box to furnish the compliance. These are called acoustic suspension speakers and must be used only in airtight enclosures. They furnish extended bass response in a small size and are popular in compact enclosures called "bookshelf systems".
A: You're right about the cone (or, more specifically, the outside edge of the cone) acting as spring. The mass is that of the coil, plus the cone, which is usually firmly attached to the coil.
Such a system, if only what I've described, would have a natural frequency given by $f=\frac1{2\pi} \sqrt{\frac km}$, in which $k$ is the force per unit displacement for the spring, and this would be a most undesirable feature. It would mean than when 'driven' with alternating currents through its coil the cone would vibrate with greater amplitude at the natural frequency and others close to it, than at other frequencies, so distorting the sound (for example making speech or music sound 'boomy').
Fortunately the cone encounters a lot of air resistance as it moves, and his has the effect of 'flattening' the resonance curve, so that the response to the natural frequency isn't so exaggerated after all. The effect is called 'damping'. No doubt there are other features of loudspeakers that improve the flatness of their response. [It is also possible that with modern loudspeakers the natural frequency is sub-audible.]
A: The "mass" is related to the mass of the cone, increased by the mass of whatever metallic parts are fixed to the cone, and are what the currents in the coils directly act on. However, not the whole actual mass of the cone counts as "mass". The "spring" is computed as the restoring force divided by the displacement, with, most probably, the displacement of the center of the cone taken as reference. But if the center moves by displacement $d$, when the rim of the cone (say, at radius $R$) is zero, the displacement of an area at distance $r$ of the center is $d*(R-r)/R$, $d$ at the center $r=0$, zero at the rim $r=R$.
So the mass of such an area does not contribute to the kinetic energy as it stands, but with a reduction factor of $(1-r/R)^2$.
If the surface density of mass of the cone were a constant  the global reduction factor would be $1/6$ (trust me for the calculation), so the "effective mass" would be
$M_{eff}=M_{cone}/6+M_{fixed}$ where $M_{fixed}$ is the mass of whatever is fixed at the center of the cone to move it in accordance to the currents in the coil.
However I am a theoretical physicist, not an acoustician. I suppose that the surface density of mass of the cone is not a constant, it is optimised for best rendition, specialists would know exactly how. So the reduction factor is probably not precisely 1/6, but I really do not know.
A: For a common dynamic loudspeaker, the mass is usually considered to be the cone, dust cap, and voice coils, and the spring is their suspension which consists of the surround and the spider. Figure 9 of the wikibooks on Acoustic Loudspeakers shows the "spring" action nicely.
The spring+mass model is not great, however, because speakers are damped driven harmonic oscillators, with emphasis on "damped" and "driven".  Loudspeakers are typically close to critical damping, with a total quality factor $Qts\sim 0.3-0.7$,  which is primarily due to voice coil electrical damping.  (The mechanical quality factor $Qms$ is typically an order-of-magnitude better than the electrical quality factor $Qes$.)  Approximate critical damping means the speaker is like a mass on a spring that has enough friction that it just returns to its equilibrium position without bouncing if its driving force is removed. This is desirable for speakers, because a high quality factor would correspond to a narrow frequency response, but what we usually want is a flat frequency response across a wide range of frequencies.
