DERevX2 - Miscellaneous Topics A Given a undamped...

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DE Review Exam 2 (Sections 4.1-4.4 plus 5.1) I. Solving linear differential equations A) Homogeneous equations with constant coefficients Use y = e mx and get the auxiliary eqn. B) Nonhomogenous equations y = y c + y p To get y p use the method of undetermined coefficients What form would be assumed for y p ? (without solving for the coefficients. II. Application to spring-mass systems and series circuits. A) simple harmonic motion, m d 2 x dt 2 + kx = 0 B) damped oscillator, m d 2 x dt 2 + β dx dt + kx = 0 C) forced,damped oscillator, m d 2 x dt 2 + β dx dt + kx = f(t) D) series circuit L d 2 q dt 2 + R dq dt + 1 C q = E ( t ) Chapter 4 review: 2,3,7a,9,1011,15,16,18,25,29,31 Chapter 5 review: 2,3,5 ,7,8,12,14,15,17,19,21
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Unformatted text preview: Miscellaneous Topics A) Given a undamped spring-mass system be able to find the period without completely solving the DE. B) Given a spring-mass system with damping be able to decide if it underdamped,citically damped,or overdamped and sketch. C Be able to solve equations with parameters(constants without specifc values) Ay'' + By = 0 where A,B are positive. Problem: Suppose a spring mass system has a mass of 1 unit, a spring constant of 4 and a damping coefficient of 5. If the mass has the initial conditions x(0) = 2 and x´(0) = 1. Make a rough sketch of the equation of motion without solving the DE....
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