University:
Massachusetts Institute of Technology
Course:
16.01 | Unified Engineering I, II, III, & IV
Academic year:

2023
Views:

294

Pages:

7
Author:

octantlqc7l

RC Circuit Step Response I Find the differential equation that describes the circuit below: e 1Ω + + u(t) – 2Ω y(t) 1F – 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−1.5t σ(t) If the input to the system is u(t) = e−t σ(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−τ σ(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, � ∞ e−1.5(t−τ ) σ(t − τ )e−τ σ(τ ) dτ y(t) = −∞ ? � = 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. −∞ � 7. 0 0 Limits of Integration I In the integral, � ∞ e−1.5(t−τ ) σ(t − τ )e−τ σ(τ ) dτ y(t) = −∞ ? � = 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 � 5. ♥ 0 � 0 6. −∞ � 7. 0 0 t Limits of Integration II In the integral, � ∞ e−1.5(t−τ ) σ(t − τ )e−τ σ(τ ) dτ y(t) = −∞ ? � = 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. −∞ � 7. 0 0 Limits of Integration II In the integral, � ∞ e−1.5(t−τ ) σ(t − τ )e−τ σ(τ ) dτ y(t) = −∞ ? � = 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. −∞ � 7. ♥ 0 0