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  1. Lecture 1: Mathematical Modeling and Physics (PDF) Lectures 2–3: Simple Harmonic Oscillator, Classical Pendulum, and General Oscillations (PDF) Lecture 4: Damped Oscillations (PDF)

    • Instructor Insights

      Those who have some exposure to physics (e.g., one class in...

    • Physics

      MIT OpenCourseWare is a web based publication of virtually...

    • Developing the Courses

      In the section below, Dr. Mobolaji Williams explains how he...

    • Lecture 7

      Introduction to Oscillations and Waves . Menu. More Info...

  2. Oscillations. David Morin, morin@physics.harvard.edu. A wave is a correlated collection of oscillations. For example, in a transverse wave traveling along a string, each point in the string oscillates back and forth in the transverse direc-tion (not along the direction of the string).

  3. Figure 4.1: Harmonic Oscillation of a mass at a spring. At the maximum elongation the spring is pulling on the mass. The mass gets accelerated towards the equilibrium position. At the equilibrium position the acceleration is zero and the velocity of the mass reaches its maximum.

  4. The simplest type of oscillations are related to systems that can be described by Hooke’s law, F = −kx, where F is the restoring force, x is the displacement from equilibrium or deformation, and k is the force constant of the system.

  5. Lecture 1: Periodic Oscillations, Harmonic Oscillators Lecture 2: Damped Free Oscillators Lecture 3: Driven Oscillators, Transient Phenomena, Resonance

  6. 1. One of the most important examples of periodic motion is simple harmonic motion (SHM), in which some physical quantity varies sinusoidally. Suppose a function of time has the form of a sine wave function, y(t) = Asin(2πt / T ) (23.1.1) where A > 0 is the amplitude (maximum value).

  7. A Driven Damped Oscillator: the Equation of Motion.....16 The Steady State Solution and Initial Transient Behavior.................................................................................16 Using Complex Numbers to Solve the Steady State Equation Easily.................................................................17

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