Vin Ra Im Determine the transfer function Dm N₂ Ow(s) Vin(s) N₁ DOD Js Ds for this system. Jw Ow

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In the given diagram, there is a system that consists of various mechanical and electrical components, used to study transfer function determination.

### Components:

1. **Electrical Circuit**:
   - **Vin**: Represents the input voltage source.
   - **Ra**: Resistor connected in series with the voltage source.

2. **Mechanical Components**:
   - **Jm**: Inertia of the motor shaft.
   - **Dm**: Damping factor associated with the motor.
   - **N1/N2**: Gear ratio between the two shafts.
   - **Js**: Inertia of the second shaft.
   - **Ds**: Damping factor for the second shaft.
   - **Jw**: Inertia of the wheel, which is driven by the system.
   - **θw**: Angular displacement of the wheel.

### Diagram Explanation:

- The electrical input (Vin) is supplied through a resistor (Ra) to a motor represented by the circle.
- The motor is mechanically connected to a shaft with inertia (Jm) and damping (Dm).
- The shaft connects to another shaft through a gear system with a ratio of N1/N2.
- The second shaft exhibits its own inertia (Js) and damping (Ds).
- Finally, this second shaft drives a wheel with inertia (Jw) to produce an angular displacement (θw).

**Objective**: Determine the transfer function, which is expressed as θw(s)/Vin(s), using the system's parameters and interactions between electrical and mechanical components.

This transfer function will represent the ratio of the output angular displacement of the wheel to the input voltage, indicating the dynamic behavior of the system.
Transcribed Image Text:In the given diagram, there is a system that consists of various mechanical and electrical components, used to study transfer function determination. ### Components: 1. **Electrical Circuit**: - **Vin**: Represents the input voltage source. - **Ra**: Resistor connected in series with the voltage source. 2. **Mechanical Components**: - **Jm**: Inertia of the motor shaft. - **Dm**: Damping factor associated with the motor. - **N1/N2**: Gear ratio between the two shafts. - **Js**: Inertia of the second shaft. - **Ds**: Damping factor for the second shaft. - **Jw**: Inertia of the wheel, which is driven by the system. - **θw**: Angular displacement of the wheel. ### Diagram Explanation: - The electrical input (Vin) is supplied through a resistor (Ra) to a motor represented by the circle. - The motor is mechanically connected to a shaft with inertia (Jm) and damping (Dm). - The shaft connects to another shaft through a gear system with a ratio of N1/N2. - The second shaft exhibits its own inertia (Js) and damping (Ds). - Finally, this second shaft drives a wheel with inertia (Jw) to produce an angular displacement (θw). **Objective**: Determine the transfer function, which is expressed as θw(s)/Vin(s), using the system's parameters and interactions between electrical and mechanical components. This transfer function will represent the ratio of the output angular displacement of the wheel to the input voltage, indicating the dynamic behavior of the system.
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