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Welcome to the Fundamentals of Mathematics for Engineers Lab ENGR 2194 Lab # 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals Car Amplifier and Concert Audio Equipment Real-World Example Related to Topic! Electrical engineers commonly use: • • Electrical signals (e.g., waveforms) Electrical equipment and instrumentation (e.g., oscilloscope) Today's Learning Objectives After today's lab, students will be able to: 1. Discuss the properties of sinusoids 2. Describe the relationships between sinusoid characteristics 3. Explain sinusoidal addition 4. Use a function generator 5. Obtain measurements using an oscilloscope Sinusoidal Relationships General Equation • 𝑥(𝑡) = 𝐴𝑠𝑖𝑛(𝜔𝑡 + 𝜙) Normal Frequency 1 • 𝑓 =𝑇 Angular Frequency • 𝜔 = 2𝜋𝑓= Time Shift • 𝑡𝑆 = ∅ 2𝜋𝑓 2𝜋 𝑇 New Equipment Inductors Capacitors Function Generator Oscilloscope Data Acquisition System Oscilloscope Reading a Circuit Diagram MATLAB Functions (e.g., “sqrt”) Plotting • Multiple graphs Commands (e.g., “hold on”) • Line specifiers • Legend Important Takeaways Essential to Engineers: • Algebra • Linear and quadratic equations • Sinusoidal relationships • Frequency, period, time shift • Electrical equipment and instrumentation • Capacitors • Inductors • Function Generator • Oscilloscope • Technical Computing MATLAB Preview of Next Lab Systems of Equations in Engineering: The TwoLoop Circuit • Matrices • Cramer’s Rule