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A system with an input x(t), and output y(t) is described by the relation y(t) = tx(t). The system is
- a)linear, time invariant and stable
- b)linear, time varying, un stable
- c)non linear, time invariant, stable
- d)non linear, time varying, unstable
Correct answer is option 'B'. Can you explain this answer?
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Linear or Nonlinear?
The system described by y(t) = tx(t) is linear because it satisfies the principle of superposition. This means that if we have two inputs x1(t) and x2(t), and corresponding outputs y1(t) and y2(t), then for any constants a and b, the output corresponding to the input ax1(t) + bx2(t) will be ay1(t) + by2(t).
Time Invariant or Time Varying?
The system is time varying because the output y(t) is directly dependent on the time variable t. If we change the input x(t) at a different time, the output will also change accordingly.
Stable or Unstable?
The system described by y(t) = tx(t) is unstable because the output y(t) grows without bound as t increases. This means that if we apply a bounded input x(t) to the system, the output will become unbounded.
Conclusion
Therefore, the correct answer is option B: Linear, time varying, unstable.
The system described by y(t) = tx(t) is linear because it satisfies the principle of superposition. This means that if we have two inputs x1(t) and x2(t), and corresponding outputs y1(t) and y2(t), then for any constants a and b, the output corresponding to the input ax1(t) + bx2(t) will be ay1(t) + by2(t).
Time Invariant or Time Varying?
The system is time varying because the output y(t) is directly dependent on the time variable t. If we change the input x(t) at a different time, the output will also change accordingly.
Stable or Unstable?
The system described by y(t) = tx(t) is unstable because the output y(t) grows without bound as t increases. This means that if we apply a bounded input x(t) to the system, the output will become unbounded.
Conclusion
Therefore, the correct answer is option B: Linear, time varying, unstable.
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A system with an input x(t), and output y(t) is described by the relat...
Linear, time varying, un stable
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A system with an input x(t), and output y(t) is described by the relation y(t) = tx(t). The system isa)linear, time invariant and stableb)linear, time varying, un stablec)non linear, time invariant, stabled)non linear, time varying, unstableCorrect answer is option 'B'. Can you explain this answer?
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