Classical Mechanics

  1. Oscillatory Motion
    1. Simple Harmonic Motion
      1. Characteristics of SHM
        1. Restoring Force Proportional to Displacement
          1. Sinusoidal Motion
          2. Mathematical Description
            1. Differential Equation
              1. General Solution
              2. The Mass-Spring System
                1. Equation of Motion
                  1. Period and Frequency
                    1. T = 2π√(m/k)
                    2. Amplitude and Phase
                    3. The Simple Pendulum
                      1. Small Angle Approximation
                        1. Period of Oscillation
                          1. T = 2π√(L/g)
                          2. Limitations of Approximation
                          3. The Physical Pendulum
                            1. Moment of Inertia Effects
                              1. Parallel Axis Theorem Application
                              2. Energy in Simple Harmonic Motion
                                1. Kinetic and Potential Energy Exchange
                                  1. Total Energy Conservation
                                    1. Energy-Position Relationships
                                  2. Damped Oscillations
                                    1. Types of Damping
                                      1. Light Damping
                                        1. Critical Damping
                                          1. Heavy Damping
                                          2. Mathematical Description
                                            1. Damping Coefficient
                                              1. Modified Differential Equation
                                              2. Exponential Decay
                                                1. Amplitude Reduction
                                                  1. Quality Factor
                                                2. Forced Oscillations and Resonance
                                                  1. Driving Forces
                                                    1. Sinusoidal Driving Force
                                                    2. Resonance Phenomenon
                                                      1. Natural Frequency Matching
                                                      2. Amplitude Response
                                                        1. Frequency Dependence
                                                          1. Resonance Curves
                                                          2. Phase Relationships
                                                            1. Driving Force and Response

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                                                        12. Fluid Mechanics