#AP Physics C: Mechanics - Unit 6: Oscillations Study Guide 🚀

Welcome to Unit 6! This unit is all about oscillations, which are back-and-forth motions you see everywhere. We'll cover simple harmonic motion (SHM), springs, pendulums, and even touch on wave motion. Think of it as a deep dive into repeating patterns of motion. Let's get started!

This unit makes up about 4-6% of the exam. While it's not the biggest topic, the concepts are crucial and often appear in combined problems. Spend time understanding the core ideas, especially SHM.

#Unit Overview

#The Big Question:

How do restoring forces predict and lead to harmonic motion? 💡

#Key Topics:

• Simple Harmonic Motion (SHM)
• Springs
• Pendulums
• Energy in SHM
• Resonance

#Exam Breakdown:

• Exam Weight: 4-6%
• Class Time: 4-7 class periods (45 minutes each)
• Practice: 20 MCQs and 2 FRQs in AP Classroom

#Key Vocabulary

• Simple Harmonic Motion (SHM): Motion where the restoring force is proportional to displacement and acts in the opposite direction. Think of it as a perfect back-and-forth motion.
• Oscillation: The back-and-forth movement of an object around its equilibrium position.
• Amplitude (A): The maximum displacement from the equilibrium position.
• Period (T): Time for one complete cycle of motion. Measured in seconds.
• Frequency (f): Number of cycles per second. Measured in Hertz (Hz). $f = \frac{1}{T}$
• Restoring Force: Force that pulls an object back to its equilibrium. Always points towards equilibrium.
• Spring Constant (k): Measure of a spring's stiffness. Higher k means a stiffer spring.
• Angular Frequency (ω): Rate of oscillation in radians per second. $ω = 2πf = \frac{2π}{T}$
• Phase Angle (φ): Initial angle of the oscillation at t=0. Determines the starting position.
• Resonance: When an object vibrates with maximum amplitude because of an external force at its natural frequency.

#Unit Questions to Ponder:

1. How does mass and spring constant affect the period of a mass-spring system?
2. How do string length and gravity affect the period of a simple pendulum?
3. How does energy change during SHM?
4. How does initial displacement affect the amplitude of SHM?
5. What is resonance and how does it occur?

#6.1 Simple Harmonic Motion (SHM)

#What is SHM?

Simple harmonic motion is a special type of periodic motion where the restoring force is directly proportional to the displacement and acts opposite to the displacement. This results in a smooth, sinusoidal motion. Think of a perfect swing or a mass bobbing up and down on a spring.

#The SHM Equation

The position of an object in SHM is described by:

$$x(t) = A \cos(ωt + φ)$$

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