# Analogy between mechanical system and electrical system

This page compares analogy between mechanical system vs electrical system and mentions difference between mechanical system and electrical system.

**Introduction**:
Two systems viz. mechanical and electrical are analogous when their differential equations are same.
They are physically different to each other as shown in the figure.

## Mechanical System

• The figure depicts mechanical system with block of mass ('m') and spring. Here 'B' is damping, 'K' is spring constant and 'X' is
the displacement due to Force ('F').

• The second order differential equation of the system can be written as follows.

➨ F = M*d^{2}x/dt^{2} + B*dx/dt + K*x ....Equation-(1)

## Electrical System

• The figure depicts Series LCR electrical system.

• It consists of resistor (R), inductor (L) and capacitor (C) all connected in series.

• When input voltage (V) is applied across its terminal, current (i) flows through it.

• Applying kirchhoff voltage law to the loop we will get equation as follows.

• V = R*i + L*di/dt + (1/C)*∫i*dt

• Substituting (dq/dt) in place of "i" in above equation, we get differential equation of electrical system as follows.

➨ V = R*dq/dt + L * d^{2}q/dt^{2} + q/C

➨ Rearranging we get, V = L * d^{2}q/dt^{2} + R*dq/dt + q/C ....Equation-(2)

## Difference between mechanical system and electrical system

Following table mentions difference between mechanical system and electrical system by comparing their analogies.

Mechanical system |
Electrical system |
---|---|

Force (F) | Voltage (V) |

Mass (M) | Inductance (L) |

Frictional Coefficient (B) | Resistance (R) |

Spring Constant (K) | Reciprocal of Capacitance (1/C) |

Displacement (x) | Charge (q) |

Velocity (v) | Current (i) |

## Analogy between mechanical oscillator and electrical oscillator

Also refer Mechanical Oscillator vs Electrical Oscillator >> which mentions analogy between mechanical oscillator and electrical oscillator.

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