The input and the output of a stable and causal LTI system are related by the dif- ferential equation d²y(t) dt² +6dy(t) dt + 8y(t) = 2x(t) (a) Find the impulse response of this system. (b) What is the response of this system if x(t) = te−2tu(t)? (c) Repeat part (a) for the stable and causal LTI system described by the equation d²y(t) +√2dy(t) ¸d²x(t) + y(t) == 2 - 2x(t) dt² dt dt²

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This is a practice question from the Signal and Systems course of my Electrical Engineering Program.

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The input and the output of a stable and causal LTI system are related by the dif-
ferential equation
d²y(t)
dt²
+6dy(t)
dt
+ 8y(t) = 2x(t)
(a) Find the impulse response of this system.
(b) What is the response of this system if x(t) = te−2tu(t)?
(c) Repeat part (a) for the stable and causal LTI system described by the equation
d²y(t) +√2dy(t)
¸d²x(t)
+ y(t)
== 2
- 2x(t)
dt²
dt
dt²
Transcribed Image Text:The input and the output of a stable and causal LTI system are related by the dif- ferential equation d²y(t) dt² +6dy(t) dt + 8y(t) = 2x(t) (a) Find the impulse response of this system. (b) What is the response of this system if x(t) = te−2tu(t)? (c) Repeat part (a) for the stable and causal LTI system described by the equation d²y(t) +√2dy(t) ¸d²x(t) + y(t) == 2 - 2x(t) dt² dt dt²
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