ENGR 205 - Fall
Unit 6 Study Guide
Section Pages Content
4.10 223-229 Forced Vibrations, Resonance and Beats (Amplitude
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
A1. Find the equation of motion for a given damped, forced vibration systems.
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
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 )
as a product of a slowly varying sine function sin( 𝜔 − 𝛾2) and a more rapidly varying
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.
B7. Convert a given 𝑛 order D.E. with specified initial