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If the system is initially relaxed at time n=0 and memory equals to zero, then the response of such state is called as:
- a)Zero-state response
- b)Zero-input response
- c)Zero-condition response
- d)None of the mentioned
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the system is initially relaxed at time n=0 and memory equals to ze...
Explanation: The memory of the system, describes, in some case, the ‘state’ of the system, the output of the system is called as ‘zero-state response’.
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If the system is initially relaxed at time n=0 and memory equals to ze...
Zero-state response:
The zero-state response refers to the response of a system when it is initially relaxed at time n=0 and the memory of the system is equal to zero. It is the response of the system to an input signal when there is no initial energy stored in the system.
Explanation:
When a system is initially relaxed, it means that there is no energy stored in the system at time n=0. This implies that there are no initial conditions or memory of the system when it is at rest.
The response of the system in this state is called the zero-state response. It is solely determined by the input signal applied to the system. The zero-state response does not take into account any prior information about the system, such as the initial conditions or the history of the input signal.
In other words, the zero-state response is the response of the system to the input signal without considering the system's initial conditions. It describes how the system reacts to the input signal when it starts from a state of rest with no stored energy.
Examples:
1. Consider a simple electrical circuit consisting of a resistor and a capacitor connected in series. If we apply a step input voltage to this circuit, the system will respond by charging the capacitor. The initial response of the system, when the capacitor is discharged and the circuit is at rest, is the zero-state response.
2. In the case of a mechanical system, such as a mass-spring-damper system, the zero-state response would be the response of the system when it is at rest, with no initial displacement or velocity.
Conclusion:
The zero-state response is the response of a system when it is initially relaxed at time n=0 and has no initial energy stored. It describes how the system reacts to an input signal without considering the system's initial conditions or history.
The zero-state response refers to the response of a system when it is initially relaxed at time n=0 and the memory of the system is equal to zero. It is the response of the system to an input signal when there is no initial energy stored in the system.
Explanation:
When a system is initially relaxed, it means that there is no energy stored in the system at time n=0. This implies that there are no initial conditions or memory of the system when it is at rest.
The response of the system in this state is called the zero-state response. It is solely determined by the input signal applied to the system. The zero-state response does not take into account any prior information about the system, such as the initial conditions or the history of the input signal.
In other words, the zero-state response is the response of the system to the input signal without considering the system's initial conditions. It describes how the system reacts to the input signal when it starts from a state of rest with no stored energy.
Examples:
1. Consider a simple electrical circuit consisting of a resistor and a capacitor connected in series. If we apply a step input voltage to this circuit, the system will respond by charging the capacitor. The initial response of the system, when the capacitor is discharged and the circuit is at rest, is the zero-state response.
2. In the case of a mechanical system, such as a mass-spring-damper system, the zero-state response would be the response of the system when it is at rest, with no initial displacement or velocity.
Conclusion:
The zero-state response is the response of a system when it is initially relaxed at time n=0 and has no initial energy stored. It describes how the system reacts to an input signal without considering the system's initial conditions or history.
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