Side-by-side comparison
| Parameter | Electrical | Mechanical Analogy |
|---|---|---|
| Analogy type | Force-Voltage (series) analogy | Force-Current (parallel) analogy |
| Force / Torque maps to | Voltage V | Current I |
| Velocity maps to | Current I | Voltage V |
| Mass m maps to | Inductance L (V = L di/dt ↔ F = m dv/dt) | Capacitance C |
| Damper B maps to | Resistance R | Conductance G = 1/R |
| Spring K maps to | Reciprocal of capacitance 1/C | Reciprocal of inductance 1/L |
| Displacement x maps to | Charge q | Flux linkage λ |
| Governing equation | mx' + Bx' + Kx = F ↔ Lq' + Rq' + q/C = V | mx' + Bx' + Kx = F ↔ Cv' + Gv' + v/L = I |
| Preferred for | Series RLC circuit analysis, impedance methods | Parallel RLC, node analysis, admittance methods |
Key differences
In the force-voltage analogy, a mass-spring-damper system with F = mx″ + Bx′ + Kx maps to a series RLC circuit with V = Lq″ + Rq′ + q/C, so m ↔ L, B ↔ R, K ↔ 1/C. In the force-current analogy, the same mechanical system maps to a parallel RLC circuit with I = Cv″ + Gv′ + v/L, so m ↔ C, B ↔ G, K ↔ 1/L. The force-voltage analogy is more commonly used in Indian university syllabi. Transfer function derivation becomes identical to impedance analysis once the analogy is established, reducing mechanical problems to Z(s) = F(s)/V(s) calculations.
When to use Electrical
Use the force-voltage (series) analogy when writing the differential equation of a mechanical system and converting it to a transfer function — a vehicle suspension analysis maps mass, spring, and damper to L, C, and R in a series loop, then KVL gives the equation directly.
When to use Mechanical Analogy
Use the force-current (parallel) analogy when the mechanical system has elements connected in parallel (e.g., multiple springs in parallel) — the node voltage in the equivalent circuit directly represents velocity, simplifying the KCL equations.
Recommendation
For exam problems, always start by identifying whether the mechanical elements are in series or parallel, then choose the matching electrical analogy and write the circuit equation — this is faster than deriving the mechanical differential equation from scratch.
Exam tip: Examiners ask you to draw the equivalent electrical circuit for a given mechanical system (mass-spring-damper) and state the element correspondence — always clearly label which electrical component corresponds to mass, spring, and damper.
Interview tip: Interviewers expect you to write the differential equation for both the mechanical and equivalent electrical system and show they are mathematically identical, demonstrating understanding of the analogy rather than just memorising the mapping table.