Similarity between RLC circuit and spring with damping

Fu-Kwun Hwang

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on: October 11, 2009, 05:20:56 pm » posted from:Taipei,T\'ai-pei,Taiwan

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 $m\frac{d^2y}{dt^2}+b\frac{dy}{dt}+ky=mg$

For a RLC circuit with DC source Vc:
The above system can be described with
$Vc=V_L+V_R+V_C$ or $L \frac{d^2Q}{dt^2}+I\frac{dQ}{dt}+\frac{Q}{C}=Vc$ ,
where $I=\frac{dQ}{dt}, V_R=I R, V_C=Q/C , V_L=L\frac{dI}{dt}$

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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