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A continuous time LTI system is described by
$${{{d^2}y\left( t \right)} \over {d{t^2}}} + 4{{dy\left( t \right)} \over {dt}} + 3y\left( t \right) = 2{{dx\left( t \right)} \over {dt}} + 4x\left( t \right)$$
Assuming zero initial conditions, the response y(t) of the above system for the input x(t) = e-2tu(t) is given by

A continuous time LTI system is described by
$${{{d^2}y\left( t \right)} \over {d{t^2}}} + 4{{dy\left( t \right)} \over {dt}} + 3y\left( t \right) = 2{{dx\left( t \right)} \over {dt}} + 4x\left( t \right)$$
Assuming zero initial conditions, the response y(t) of the above system for the input x(t) = e-2tu(t) is given by Correct Answer (e<sup>-t</sup> - e<sup>-3t</sup>)u(t)

Related Questions

Consider a system whose input r and output y are related by the equation $$y\left( t \right) = \int\limits_{ - \infty }^\infty {x\left( {t - \tau } \right)} h\left( {2\tau } \right)d\tau $$
Signal Processing mcq question image
Where h(t) is shown in the graph
Which of the following four properties are possessed by the system? BIBO: Bounded input gives a bounded output
Causal: The system is causal.
LP : The system is low pass.
LTI: The system is linear and time-invariant.
The transfer function of a discrete time LTI system is given by
$$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$
Consider the following statements:
S1 : The system is stable and causal for
$$ROC:\left| z \right| > {1 \over 2}$$
S2 : The system is stable but not causal for
$$ROC:\left| z \right| S3 : The system is neither stable nor causal for
$$ROC:{1 \over 4} Which one of the following statements is valid?
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If h(n) is the impulse response of an LTI system and hI(n) is the impulse response of the inverse LTI system, then which of the following is true?
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Below are given two sets, Set - I which gives modalities of operant conditioning and Set - II which provides the types of reinforcement, the types of responses (responses made or withheld) and the presence or absence of cue. Match the two sets and indicate your answer by choosing from the code : Set - I (Modalities of operant conditioning procedures) Set – II           (Conditions and contexts) (a) Reward training (i) Positive reinforcement, response made, with cue present (b) Escape training (ii) Positive reinforcement, response withheld with cue absent (c) Discriminated omission training   (iii) Positive reinforcement, response made with cue absent (d) Active avoidance   (iv) Negative reinforcement, response made with training (e) Punishment training (v) Positive reinforcement, response withheld with cue present   (vi) Negative reinforcement, response withheld with cue absent  
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