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MIT 16 01 - RC Circuit Step Response I

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RC Circuit Step Response I Find the differential equation that describes the circuit below: –+1Ω2Ω 1Fu(t)y(t)e–+Press “1” on your PRS remote when you are finished.RC Circuit Step Response I The differential equation that describes the circuit is d e1(t) + 1.5e1(t) = u(t)dt My answer 1. Was completely correct 2. Was mostly correct, with one or two minor errors 3. Had many errors 4. Was completely incorrect� Limits of Integration The system G has impulse respnse g(t) = e−1.5tσ(t) If the input to the system is u(t) = e−tσ(t) the output can be found using the convolution integral as ∞ y(t) = g(t − τ)u(τ) dτ �−∞ ∞ = e−1.5(t−τ)σ(t − τ)e−τσ(τ) dτ �−∞ = e? −1.5(t−τ)e−τ dτ ? What should the limits of integration be if t > 0?� � � � � � Limits of Integration I In the integral, ∞ y(t) = e−1.5(t−τ)σ(t − τ)e−τσ(τ) dτ �−∞ = e? −1.5(t−τ)e−τ dτ ? what should the limits of integration be if t > 0? ∞1. −∞ t 2. −∞ ∞3. t ∞4. 0 t 5. 0 � 0 6. −∞ � 0 7. 0� � � � � � Limits of Integration I In the integral, ∞ y(t) = e−1.5(t−τ)σ(t − τ)e−τσ(τ) dτ �−∞ = e? −1.5(t−τ)e−τ dτ ? what should the limits of integration be if t > 0? The correct answer is: ∞1. −∞ t 2. −∞ ∞3. t ∞4. 0 t 5. ♥ 0 � 0 6. −∞ � 0 7. 0� � � � � � Limits of Integration II In the integral, ∞ y(t) = e−1.5(t−τ)σ(t − τ)e−τσ(τ) dτ �−∞ = e? −1.5(t−τ)e−τ dτ ? what should the limits of integration be if t < 0? ∞1. −∞ t 2. −∞ ∞3. t ∞4. 0 t 5. 0 � 0 6. −∞ � 0 7. 0� � � � � � Limits of Integration II In the integral, ∞ y(t) = e−1.5(t−τ)σ(t − τ)e−τσ(τ) dτ �−∞ = e? −1.5(t−τ)e−τ dτ ? what should the limits of integration be if t < 0? The correct answer is: ∞1. −∞ t 2. −∞ ∞3. t ∞4. 0 t 5. 0 � 0 6. −∞ � 0 7. ♥


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MIT 16 01 - RC Circuit Step Response I

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