Force and circuit analogies question type

You can have a look at the suggested link. But I should say that the two systems are not exactly analogous because in the mechanical one there is a force which does not have a counterpart in the electrical circuit. I thinks that a voltage generator is missing in the electrical circuit.

Going briefly into details, to have an electro-mechanical analogy you have to establish which mechanical quantity is analogous to the electrical quantity. There are at least two different ways. One says that the force $F$ is analogous of the voltage $V$ and the velocity $u$ is the analogous of the current $I$ (and as a consequence the displacement $x$ is analogous to the charge $q$). With this convention the mechanical mass $m$ corresponds to the inductance $L$, and the spring compliance $1/k$ to the capacitance $C$, the dashpot $gamma$ to a resistance $R$.

Given all that, the two systems are governed by the same ordinary differentalia equation. For the mass-spring system driven by the force $F$ you have $$ mdfrac{d^2x}{dt^2}+kx = F $$

While the equation of the circuit using the charge $q$ as the variable is: $$ Ldfrac{d^2q}{dt^2}+dfrac{1}{C}q = V $$ (Please note that in your schematic a voltage generator is missing).

Comparing the two equations you can see the analogies I've described above.

Try writing down the motion in terms of $x$ of the spring system, and also the behavior in terms of $q$ of the LC circuit (use KVL). You should see some striking similarities that lead to the electrical-mechanical analogies mentioned by Bob D.