Find a particular solution for the given differential equation. d²q dq La +Ra + q = Vosin (wt) dt dt
Find a particular solution for the given differential equation. d²q dq La +Ra + q = Vosin (wt) dt dt
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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![**Problem Statement:**
Find a particular solution for the given differential equation.
**Differential Equation:**
\[ L \frac{d^2q}{dt^2} + R \frac{dq}{dt} + \frac{1}{C} q = V_0 \sin (\omega t) \]
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**Explanation:**
This equation represents a second-order linear differential equation with constant coefficients, often used to model electrical circuits involving inductance (\(L\)), resistance (\(R\)), and capacitance (\(C\)). The term \(V_0 \sin (\omega t)\) on the right side represents an external sinusoidal driving force. The goal is to find a particular solution \(q(t)\) that satisfies this equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89a69b77-6859-4c30-95b3-e6df6014c589%2F947dc4c6-03dd-46e2-ac51-eddceb6f639f%2Fuefnym_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find a particular solution for the given differential equation.
**Differential Equation:**
\[ L \frac{d^2q}{dt^2} + R \frac{dq}{dt} + \frac{1}{C} q = V_0 \sin (\omega t) \]
---
**Explanation:**
This equation represents a second-order linear differential equation with constant coefficients, often used to model electrical circuits involving inductance (\(L\)), resistance (\(R\)), and capacitance (\(C\)). The term \(V_0 \sin (\omega t)\) on the right side represents an external sinusoidal driving force. The goal is to find a particular solution \(q(t)\) that satisfies this equation.
Expert Solution
Step 1: Use the formula f(D^2)y =sinax
We will use the following formula to get the particular solution of the above differential equation
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