m351 - Project PHYSNET Physics Bldg. Michigan State...

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Unformatted text preview: Project PHYSNET Physics Bldg. Michigan State University East Lansing, MI • • • MISN-0-351 EULER’S METHOD FOR COUPLED DIFFERENTIAL EQUATIONS; RLC CIRCUITS q(t) q(t + t) D t t + ½ t D t + t D a b c 1 EULER’S METHOD FOR COUPLED DIFFERENTIAL EQUATIONS; RLC CIRCUITS by Robert Ehrlich 1. Euler’s Method a. Original Euler’s Method .................................1 b. Improved Euler’s Method ...............................1 c. The RLC Circuit ....................................... 3 d. Applying the Two Euler Methods to RLC Circuits ...... 4 2. Several Exact Solutions a. Zero Applied Voltage ................................... 5 b. Sinusoidal Applied Voltage .............................. 7 c. Resonance in RLC Circuit ..............................8 d. Error Analysis .........................................10 3. Computer Implementation a. Input .................................................. 10 b. Output ................................................ 11 4. A Project: Examine Accuracy a. Accuracy For Free Oscillations ......................... 11 b. Accuracy For Forced Oscillations, Resonances .......... 12 Acknowledgments .......................................... 12 A. Fortran, Basic, C++ Programs ........................12 ID Sheet: MISN-0-351 Title: Euler’s Method for Coupled Differential Equations; RLC Circuits Author: R. Ehrlich, Physics Dept., George Mason University, Fairfax, VA 22030; (703)323-2303. Version: 3/11/2002 Evaluation: Stage 0 Length: 2 hr; 20 pages Input Skills : 1. Vocabulary: inductor (MISN-0-144). 2. Describe the Euler-method algorithm for solving first-order differ- ential equations (MISN-0-350). Output Skills (Knowledge) : K1. Write an explanation of the improved Euler method for the nu- merical solution of two coupled first-order differential equations of the form dy 1 /dx = f 1 ( y 1 ,y 2 ,x ), dy 2 /dx = f 2 ( y 1 ,y 2 ,x ). Output Skills (Project) : P1. Use the improved Euler method to solve the coupled, first order differential equations for an RLC circuit for free oscillations. P2. Use the improved Euler method to solve the coupled, first-order differential equations for an RLC circuit for oscillations that are forced by a sine-wave voltage generator. External Resources (Required) : 1. A computer with BASIC or FORTRAN or C++. 3 THIS IS A DEVELOPMENTAL-STAGE PUBLICATION OF PROJECT PHYSNET The goal of our project is to assist a network of educators and scientists in transferring physics from one person to another. We support manuscript processing and distribution, along with communication and information systems. We also work with employers to identify basic scientific skills as well as physics topics that are needed in science and technology. A number of our publications are aimed at assisting users in acquiring such skills....
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This note was uploaded on 03/20/2010 for the course ENGINEERIN EE04-165 taught by Professor Nawaz during the Fall '10 term at Superior University Lahore.

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m351 - Project PHYSNET Physics Bldg. Michigan State...

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