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.
• 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)
• 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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