= Solution
The original diagram is a <series RLC circuit>, so the same <electric current> $i=\dot q$ passes through all three elements. Choose capacitor <electric charge> $q$ positive on the plate into which positive $i$ enters. <Kirchhoff's voltage law> gives
$$
V(t)=V_L+V_R+V_C=L\frac{di}{dt}+Ri+\frac qC=L\ddot q+R\dot q+\frac qC.
$$
Dividing by <inductance> $L$ gives
$$
\boxed{\ddot q+\frac RL\dot q+\frac1{LC}q=\frac{V(t)}L}.
$$
The correspondence to the <forced harmonic oscillator> is $m\leftrightarrow L$, $b\leftrightarrow R$, $k\leftrightarrow1/C$, and $x\leftrightarrow q$. The stored <energy> is $L i^2/2+q^2/(2C)$; its balance is $\dot E=Vi-Ri^2$, confirming the damping sign.
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