Classical Mechanics

11.

Oscillatory Motion

11.1.

Simple Harmonic Motion

11.1.1.

Characteristics of SHM

11.1.1.1.

Restoring Force Proportional to Displacement

11.1.1.2.

Sinusoidal Motion

11.1.2.

Mathematical Description

11.1.2.1.

Differential Equation

11.1.2.2.

General Solution

11.1.3.

The Mass-Spring System

11.1.3.1.

Equation of Motion

11.1.3.2.

Period and Frequency

11.1.3.2.1.

T = 2π√(m/k)

11.1.3.3.

Amplitude and Phase

11.1.4.

The Simple Pendulum

11.1.4.1.

Small Angle Approximation

11.1.4.2.

Period of Oscillation

11.1.4.2.1.

T = 2π√(L/g)

11.1.4.3.

Limitations of Approximation

11.1.5.

The Physical Pendulum

11.1.5.1.

Moment of Inertia Effects

11.1.5.2.

Parallel Axis Theorem Application

11.1.6.

Energy in Simple Harmonic Motion

11.1.6.1.

Kinetic and Potential Energy Exchange

11.1.6.2.

Total Energy Conservation

11.1.6.3.

Energy-Position Relationships

11.2.

Damped Oscillations

11.2.1.

Types of Damping

11.2.1.1.

11.2.1.2.

Critical Damping

11.2.1.3.

11.2.2.

Mathematical Description

11.2.2.1.

Damping Coefficient

11.2.2.2.

Modified Differential Equation

11.2.3.

Exponential Decay

11.2.3.1.

Amplitude Reduction

11.2.3.2.

11.3.

Forced Oscillations and Resonance

11.3.1.

11.3.1.1.

Sinusoidal Driving Force

11.3.2.

Resonance Phenomenon

11.3.2.1.

Natural Frequency Matching

11.3.3.

Amplitude Response

11.3.3.1.

Frequency Dependence

11.3.3.2.

Resonance Curves

11.3.4.

Phase Relationships

11.3.4.1.

Driving Force and Response

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