ENGR 205 Midterm: ENGR 205 Unit 6 Study Guide

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University of Louisville
Engineering Fundamentals
ENGR 205

ENGR 205 - Fall Unit 6 Study Guide Unit Content: Section Pages Content 4.10 223-229 Forced Vibrations, Resonance and Beats (Amplitude Modulation) 5.7 291-296 Simple Electric (RLC) Circuits 5.3 253-254 Normal Form for a System of Differential Equations 5.2 244-250 Introduction to Systems of Linear Differential Equations with Constant Coefficients, the Elimination Method 5.3 253-254 Converting an 𝑛 𝑡ℎOrder Differential Equation into a System 7.9 412-413 Solving Linear Systems with Laplace Transforms Learning objectives: A1. Find the equation of motion for a given damped, forced vibration systems. 𝛾 A2. Find the resonance frequency, 𝑟⁄2𝜋 , for a given damped, forced vibration system. A3. Determine the equation of motion for a given undamped, forced vibration system at a resonance. B4. Write the solution 𝑦(𝑡) to a given undamped system ′′ ′ √ ⁄ (𝑚𝑦 + 𝑘𝑦 = 𝐹 cos0𝛾𝑡 ,𝑦 0 = 𝑦 0 = 0 with 𝜔 − 𝛾 small (where = 𝑚 ) 𝑡 as a product of a slowly varying sine function sin( 𝜔 − 𝛾2) and a more rapidly varying 𝑡 sine function sin( 𝜔 + 𝛾 )2) B5. Given an RLC series circuit with specified voltage 𝐸(𝑡), resistance 𝑅, inductance 𝐿, capacitance 𝐶, initial charge on the capacitor 𝑞 0 , and initial current 𝐼 0 , determine the charge 𝑞 𝑡 on the capacitor, and or the current 𝐼 𝑡 in the circuit for 𝑡 > 0. B6. Solve a given system of differential equations using the elimination method. 𝑡ℎ B7. Convert a given 𝑛 order D.E. with specified initial
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