Deriving General Harmonic Motion Equations | AP Physics C: Mechanics - Unit 7 - Lesson 4C

Описание: In this AP Physics C video, we break down Simple Harmonic Motion (SHM) from the ground up. You’ll learn how oscillations work using differential equations, and how to derive the period formulas for mass-spring systems, simple pendulums, and physical pendulums—exactly the way College Board expects on the AP exam.

This lesson covers:

General harmonic motion using second-order differential equations
How SHM solutions lead to sine and cosine motion
Deriving the period of a horizontal mass-spring system
Deriving the period of a simple pendulum using torque
Understanding the small angle approximation
Physical pendulums and how rotational inertia affects the period
How to recognize SHM patterns quickly on AP exam questions

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These concepts are core topics in AP Physics C: Mechanics and show up frequently in free-response and multiple-choice questions. If you understand how these equations are derived—not just memorized—you’ll solve oscillation problems faster and with more confidence.

Chapters
00:00 Introduction to General Harmonic Motion
00:26 Deriving General Harmonic Motion Equations
00:54 Differential Equation Setup
03:03 Example: Deriving the period formula
05:21 Example: Horizontal Mass–Spring System Derivation
09:37 Example: Pendulum Period Derivation
13:27 Final Message

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