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Consider the following first-order, causal LTI differential system S₁ initially at rest: dx(t) dt (a) Calculate the impulse response h₁(t) of the system S₁. Sketch it for a = 2. S₁: dy(t) dt + ay(t) = - 2x(t), a>0 is real.

Consider the following first-order, causal LTI differential system S₁ initially at rest: dx(t) dt (a) Calculate the impulse response h₁(t) of the system S₁. Sketch it for a = 2. S₁: dy(t) dt + ay(t) = - 2x(t), a>0 is real.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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### First-Order, Causal LTI Differential System Consider the following first-order, causal LTI differential system \( S_1 \) initially at rest: \[ S_1: \frac{dy(t)}{dt} + ay(t) = \frac{dx(t)}{dt} - 2x(t), \quad a > 0 \text{ is real}. \] (a) **Problem:** Calculate the impulse response \( h_1(t) \) of the system \( S_1 \). Sketch it for \( a = 2 \).
Transcribed Image Text:### First-Order, Causal LTI Differential System Consider the following first-order, causal LTI differential system \( S_1 \) initially at rest: \[ S_1: \frac{dy(t)}{dt} + ay(t) = \frac{dx(t)}{dt} - 2x(t), \quad a > 0 \text{ is real}. \] (a) **Problem:** Calculate the impulse response \( h_1(t) \) of the system \( S_1 \). Sketch it for \( a = 2 \).
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