Which of the following is correct analogy between electrical and mechanical system for vibrating system?

Explanation:

In the context of system dynamics, both mechanical and electrical systems can be modeled to understand how they behave in response to inputs over time. These models often involve elements that have analogous properties in both domains, allowing engineers to draw parallels between them. For vibrating systems, the equivalences between mechanical and electrical systems are particularly useful for analysis and design.

Mechanical System Components:

• Mass (m): Represents the inertia of the system, resisting acceleration when a force is applied.
• Spring Stiffness (k): Represents the restoring force that acts to bring the system back to its equilibrium position.
• Damping Coefficient (c): Represents the resistive force that dissipates energy, reducing the amplitude of oscillations.
• Force (F): The external input or excitation applied to the system.

Electrical System Components:

• Inductance (L): Represents the inertia of the electrical system, resisting changes in current.
• Capacitance (C): Represents the ability to store electrical energy, analogous to the spring in a mechanical system.
• Resistance (R): Represents the resistive element that dissipates energy, analogous to the damping coefficient in a mechanical system.
• Voltage (V): The external input or excitation applied to the system.

Damping Coefficient (c) and Resistance (R):

• The damping coefficient in a mechanical system is a measure of the resistive force that opposes the motion and dissipates energy. This is analogous to resistance in an electrical system, which opposes the flow of current and dissipates electrical energy as heat. Both elements serve to reduce the amplitude of oscillations in their respective systems, thereby controlling the stability and response of the system.