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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#### 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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