A mass m attached to a vertical spring (spring constant k) in gravity field:

The above system can be described with

$ F=m a_y= mg -ky -b v_y$ or $mfrac{d^2y}{dt^2}+bfrac{dy}{dt}+ky=mg$

For a RLC circuit with DC source Vc:

The above system can be described with

$ Vc=V_L+V_R+V_C$ or $L frac{d^2Q}{dt^2}+Ifrac{dQ}{dt}+frac{Q}{C}=Vc$,

where $I=frac{dQ}{dt}, V_R=I R, V_C=Q/C , V_L=Lfrac{dI}{dt}$

The differential equation are the same for the above two systems.

So a damped spring system can be simulated with RLC circuit (or RLC circuit can be simulated with damped spring system,too!).

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