The above table on the right shows input-output (steady-state) relationsh o be identified. Knowing that the system is either first- or second-order, deter

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Subject: Mechanical Measurements

### Transcription for Educational Website

#### Input-Output Relationship for a Sensor System

The table below presents the input-output (steady-state) relationship for a sensor system that is currently unidentified. The relationship is given as follows:

| **y (input)** | **x (output)**                |
|---------------|-------------------------------|
| 1             | 8                             |
| sin(15t)      | 8.05 sin(15t - 2°)            |
| sin(60t)      | 8.90 sin(60t - 22°)           |
| sin(150t)     | 10 sin(150t - 90°)            |
| sin(900t)     | 0.23 sin(900t - 176°)         |

#### Problem Statement

Based on the above table, determine the characteristics of the sensor system. Given that the system is either a first or second-order system, answer the following questions:

(a) **Order of the System Model**:
   - Determine whether the system is of first-order or second-order.
   - Specify whether it is over-damped, critically-damped, or under-damped if it is a second-order system.
   - Provide two reasons for your determination.

(b) **Static Sensitivity**:
   - Calculate the static sensitivity of this system.

(c) **Transfer Function**:
   - Derive the transfer function for this system.

(d) **Useful Frequency Range**:
   - Calculate the useful frequency range of this system within a tolerance of ±5%.

This exercise involves analyzing the input-output data to infer the underlying dynamics of the sensor system and to determine its transfer characteristics.
Transcribed Image Text:### Transcription for Educational Website #### Input-Output Relationship for a Sensor System The table below presents the input-output (steady-state) relationship for a sensor system that is currently unidentified. The relationship is given as follows: | **y (input)** | **x (output)** | |---------------|-------------------------------| | 1 | 8 | | sin(15t) | 8.05 sin(15t - 2°) | | sin(60t) | 8.90 sin(60t - 22°) | | sin(150t) | 10 sin(150t - 90°) | | sin(900t) | 0.23 sin(900t - 176°) | #### Problem Statement Based on the above table, determine the characteristics of the sensor system. Given that the system is either a first or second-order system, answer the following questions: (a) **Order of the System Model**: - Determine whether the system is of first-order or second-order. - Specify whether it is over-damped, critically-damped, or under-damped if it is a second-order system. - Provide two reasons for your determination. (b) **Static Sensitivity**: - Calculate the static sensitivity of this system. (c) **Transfer Function**: - Derive the transfer function for this system. (d) **Useful Frequency Range**: - Calculate the useful frequency range of this system within a tolerance of ±5%. This exercise involves analyzing the input-output data to infer the underlying dynamics of the sensor system and to determine its transfer characteristics.
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