Mechanical system
m ẍ + c ẋ + kx = F(t)
x is measured from the dashed equilibrium reference. Drag the mass to prepare x₀, then press Play.
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Force–voltage: series RLC
The correspondences — live values
| Role | Mechanical | Electrical | Instantaneous correspondence |
|---|
Displacement & charge
Mechanical — solid Electrical — dashed · same numerical teaching scale
Velocity & current
The cursor is physical time. Click or drag either plot to scrub.
Storage, loss and input work
Spring and inertial storage exchange. The damper/resistor dissipates; it does not store recoverable energy. With an applied force, include input work.
Identical characteristic roots
Filled = mechanics; outlined = circuit. These roots stay fixed while time advances.
Both analogies at a glance
| Mechanical | Force–voltage | Force–current |
|---|---|---|
| Applied force F | Source voltage e | Source current Iₛ |
| Velocity v | Loop current i | Node voltage V |
| Displacement x | Charge q | Flux linkage ψ = L iL |
| Mass m | Inductance L = m | Capacitance C = m |
| Damper c | Resistance R = c | Conductance G = c; R = 1/c |
| Spring stiffness k | 1/C = k | 1/L = k |
The mappings use the stated unity numerical scales. They do not assert that a kilogram is a henry or a newton is a volt.
Sources and derivation
The diagrams and derivation are original teaching illustrations. Constitutive laws and the force–voltage mapping were checked against University of Illinois BIOE 205, Lecture 15. The force–current mapping is also documented in Virginia Tech's energy-harvesting dissertation, Table 4.1.
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