Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Question #4 (chapter La Place Transform, online)
Solve \( Y'' + Y = \sin(2t) \) using Laplace and inverse Laplace transforms.
---
### Question 5
(Use the electrical circuit differential equation - Book reference section 16.3)
\[
\frac{d^2 q}{dt^2} + \left( \frac{R}{L} \right) \frac{dq}{dt} + \left( \frac{1}{LC} \right) q = \left( \frac{1}{L} \right) E(t)
\]
Where:
- \( R \) is the resistance (in ohms),
- \( C \) is the capacitance (in farads),
- \( L \) is the inductance (in henrys),
- \( E(t) \) is the electromotive force (in volts),
- \( q \) is the charge on the capacitor (in coulombs).
Find the charge \( q \) as a function of time \( t \) for the electrical circuit described. Assume that \( q(0) = 0 \) and \( q'(0) = 0 \).
Given values:
- \( R = 20 \)
- \( C = 0.02 \)
- \( L = 1 \)
- \( E(t) = 10 \sin 5t \)
---
This will be shown on the educational website to help students understand how to apply Laplace transforms to differential equations and solve electrical circuit problems using differential equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdd3569f9-4294-4cc9-8a50-1c0c054eb5e2%2Fe6791d4a-728b-429f-bd48-0ed294cd2065%2Fbicyu89_processed.png&w=3840&q=75)
Transcribed Image Text:### Question #4 (chapter La Place Transform, online)
Solve \( Y'' + Y = \sin(2t) \) using Laplace and inverse Laplace transforms.
---
### Question 5
(Use the electrical circuit differential equation - Book reference section 16.3)
\[
\frac{d^2 q}{dt^2} + \left( \frac{R}{L} \right) \frac{dq}{dt} + \left( \frac{1}{LC} \right) q = \left( \frac{1}{L} \right) E(t)
\]
Where:
- \( R \) is the resistance (in ohms),
- \( C \) is the capacitance (in farads),
- \( L \) is the inductance (in henrys),
- \( E(t) \) is the electromotive force (in volts),
- \( q \) is the charge on the capacitor (in coulombs).
Find the charge \( q \) as a function of time \( t \) for the electrical circuit described. Assume that \( q(0) = 0 \) and \( q'(0) = 0 \).
Given values:
- \( R = 20 \)
- \( C = 0.02 \)
- \( L = 1 \)
- \( E(t) = 10 \sin 5t \)
---
This will be shown on the educational website to help students understand how to apply Laplace transforms to differential equations and solve electrical circuit problems using differential equations.
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