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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*d2x/dt2 + B*dx/dt + K*x ....Equation-(1)

Analogy between Mechanical System and Electrical System

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 * d2q/dt2 + q/C
➨ Rearranging we get, V = L * d2q/dt2 + 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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