Question #4 ( chapter La Place Transform, online) Solve Y"+ Y = Sin(2t) using La place and inverse la Place transform Transform.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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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.
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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