Math 238 Problem Set 41 Laplace Transform in Applied Problems Problem 1: Recall that an RC-series circuit can be modeled using the differential equation: dq 1 R = +79 dt E (t) Consider an RC-series circuit with a resistance of 10 and a capacitance of 0.1. The impressed voltage, as a function of time, is given by the piecewise function E(t) = {30e², (30et, 0≤t<1.5 1.5 ≤t If the charge is initially equal to 0, find an equation for the charge q (t) at time t.
Math 238 Problem Set 41 Laplace Transform in Applied Problems Problem 1: Recall that an RC-series circuit can be modeled using the differential equation: dq 1 R = +79 dt E (t) Consider an RC-series circuit with a resistance of 10 and a capacitance of 0.1. The impressed voltage, as a function of time, is given by the piecewise function E(t) = {30e², (30et, 0≤t<1.5 1.5 ≤t If the charge is initially equal to 0, find an equation for the charge q (t) at time t.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Answer key:
3
1) y = ²e² - e-t-e¹5 U(t – 1.5)[et-1.5 — e-(t−1.5)]
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2
2
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F27123adf-a73c-4bd6-998a-f82c7820ac3a%2F91ce079b-9616-4dec-8a5b-ad5395aed109%2Fwxd9heg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Answer key:
3
1) y = ²e² - e-t-e¹5 U(t – 1.5)[et-1.5 — e-(t−1.5)]
-
2
2
2
Transcribed Image Text:Math 238
Problem Set 41
Laplace Transform in Applied Problems
Problem 1: Recall that an RC-series circuit can be modeled using the differential equation:
dq
1
+
dt C 9 = E(t)
Consider an RC-series circuit with a resistance of 10 and a capacitance of 0.1. The impressed voltage, as
a function of time, is given by the piecewise function
E(t) = {30e¹,
(30et, 0≤t< 1.5
1.5 ≤ t
If the charge is initially equal to 0, find an equation for the charge q(t) at time t.
R
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