The given question is asking for various terms and values related to a differential equation and its transfer function. Let's go through each term and value one by one:
1. Differential Equation: This refers to the equation that relates the derivative(s) of a function to the function itself. In this case, the given differential equation is 45r(t) = 1c′′(t) + 2c′(t) + 9c(t). It involves the second derivative, first derivative, and the function c(t).
2. Transfer Function: A transfer function is the mathematical representation of the relationship between the input and output of a system. In this case, the transfer function is not explicitly provided in the question.
3. Damping Coefficient (α): The damping coefficient, denoted by α, represents the resistance to the motion of a system. It influences the rate at which oscillations in a system decay. However, the value of the damping coefficient is not given in the question.
4. Damping Ratio (ζ): The damping ratio, denoted by ζ, is the ratio of the actual damping coefficient to the critical damping coefficient. It provides information about the type of damping in the system. However, the value of the damping ratio is not given in the question.
5. Damped Natural Frequency (ωd): The damped natural frequency, denoted by ωd, represents the frequency at which the system oscillates when subjected to damping. Unfortunately, the value of the damped natural frequency is not provided in the question.
6. System Gain (Ks): The system gain, denoted by Ks, is the amplification factor of the input signal in the system. However, the value of the system gain is not given in the question.
7. Steady State Response Value (Css): The steady state response value, denoted by Css, refers to the final output of the system after it has reached a stable state. It is obtained by analyzing the behavior of the system over a long period of time. Unfortunately, the steady state response value is not provided in the question.
8. Response time Value at Delay Time C(td): The response time value at delay time, denoted by C(td), represents the output of the system at a specific time delay. The specific value of td is not given in the question.
9. Delay Time (td): The delay time, denoted by td, is the time it takes for the system to respond to an input signal. However, the value of the delay time is not provided in the question.
10. Response time Value at Settling Time C(ts): The response time value at settling time, denoted by C(ts), represents the output of the system at a specific settling time. The specific value of ts is not given in the question.
11. Settling Time (ts) 5%: The settling time, denoted by ts, represents the time it takes for the system's output to reach and stay within a specified percentage (5% in this case) of its final value. However, the specific value of the settling time is not provided in the question.
12. Settling Time (ts) 2%: Similar to the settling time 5%, the settling time 2% represents the time it takes for the system's output to reach and stay within a specified percentage (2% in this case) of its final value. However, the specific value of the settling time is not given in the question.
13. Response time Value at Rise Time C(tr): The response time value at rise time, denoted by C(tr), represents the output of the system at a specific rise time. The specific value of tr is not given in the question.
14. Rise Time (tr): The rise time, denoted by tr, is the time it takes for the system's output to transition from a specified percentage (e.g., 10% to 90%) of its initial value to another specified percentage (e.g., 90% to 10%) of its final value. However, the specific value of the rise time is not provided in the question.
15. Peak Time (tP): The peak time, denoted by tP, is the time it takes for the system's output to reach its maximum value. However, the specific value of the peak time is not given in the question.
16. Peak Overshoot (%MP): The peak overshoot, denoted by %MP, represents the percentage by which the system's output exceeds its final steady state value. However, the specific value of the peak overshoot is not provided in the question.
17. Response time Value at Peak Time (MP): The response time value at peak time, denoted by MP, represents the output of the system at the specific peak time. The specific value of the peak time is not given in the question.
In summary, the question provides a differential equation and asks for various terms and values related to the system described by the equation. However, specific values for the damping coefficient, damping ratio, damped natural frequency, system gain, steady state response value, delay time, settling time, rise time, peak time, peak overshoot, and response time at peak time are not provided. It is important to have these values to perform a complete analysis of the system and obtain meaningful results.