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The following differential equation demonstrates the performance of an electrical circuit for time t2 0: d²y(t) dy(t) +3 + 2y(t) = x(t) +3 dt dx(t) dt2 %3D dt where y(t) is the voltage at the output port and x(t) is the voltage applied to the input terminal at time t = 0. All initial conditions are zero. a) Show that the impulse response of the circuit is h(t) = 5e¬2t – 2e¬t. %3D b) Find the output y(t) when the input is x(t) = 1 + e¬2t by using the following two methods: i. Direct convolution y(t) = h(t)x(t – t)dr

The following differential equation demonstrates the performance of an electrical circuit for time t2 0: d²y(t) dy(t) +3 + 2y(t) = x(t) +3 dt dx(t) dt2 %3D dt where y(t) is the voltage at the output port and x(t) is the voltage applied to the input terminal at time t = 0. All initial conditions are zero. a) Show that the impulse response of the circuit is h(t) = 5e¬2t – 2e¬t. %3D b) Find the output y(t) when the input is x(t) = 1 + e¬2t by using the following two methods: i. Direct convolution y(t) = h(t)x(t – t)dr

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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The following differential equation demonstrates the performance of an electrical circuit for time t> 0: d²y(t) dy(t) +3 + 2y(t) = x(t) + 3- dt dx(t) dt2 dt where y(t) is the voltage at the output port and x(t) is the voltage applied to the input terminal at time t = 0. All initial conditions are zero. a) Show that the impulse response of the circuit is h(t) = 5e-2t – 2e-t. b) Find the output y(t) when the input is x(t) = 1 + e¬2t by using the following two methods: i. Direct convolution y(t) = h(t)x(t-t)dr %3D
Transcribed Image Text:The following differential equation demonstrates the performance of an electrical circuit for time t> 0: d²y(t) dy(t) +3 + 2y(t) = x(t) + 3- dt dx(t) dt2 dt where y(t) is the voltage at the output port and x(t) is the voltage applied to the input terminal at time t = 0. All initial conditions are zero. a) Show that the impulse response of the circuit is h(t) = 5e-2t – 2e-t. b) Find the output y(t) when the input is x(t) = 1 + e¬2t by using the following two methods: i. Direct convolution y(t) = h(t)x(t-t)dr %3D
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