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ENGR 205 Midterm: ENGR 205 Unit 6 Study Guide
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University of Louisville

Engineering Fundamentals

ENGR 205

Robinson

Summer

Description

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 π π‘βOrder 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.
πΎ
A2. Find the resonance frequency, πβ2π , 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 π¦(π‘) to a given undamped system
β²β² β² β β
(ππ¦ + ππ¦ = πΉ cos0πΎπ‘ ,π¦ 0 = π¦ 0 = 0 with π β πΎ small (where = π )
π‘
as a product of a slowly varying sine function sin( π β πΎ2) and a more rapidly varying
π‘
sine function sin( π + πΎ )2)
B5. Given an RLC series circuit with specified voltage πΈ(π‘), resistance π
, inductance πΏ,
capacitance πΆ, initial charge on the capacitor π 0 , and initial current πΌ 0 , determine
the charge π π‘ on the capacitor, and or the current πΌ π‘ in the circuit for π‘ > 0.
B6. Solve a given system of differential equations using the elimination method.
π‘β
B7. Convert a given π order D.E. with specified initial

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