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Lecture 1: Mathematical Modeling and Physics (PDF) Lectures 2–3: Simple Harmonic Oscillator, Classical Pendulum, and General Oscillations (PDF) Lecture 4: Damped Oscillations (PDF)
Lecture Notes | Introduction to Oscillations and Waves | Physics | MIT OpenCourseWare. pdf. 474 kB. RES.8-009 (Summer 2017), Lecture 8: Traveling Waves and Boundary Interactions. MIT OpenCourseWare is a web based publication of virtually all MIT course content. OCW is open and available to the world and is a permanent MIT activity.
Free oscillations occur when no external force is continuously acting on the system, so its energy remains constant. The system will oscillate at its. natural frequency. Examples of systems which experience free oscillations are: Simple pendulum - A small, dense bob that hangs from a string, which is attached to a fixed point.
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.
Simple Harmonic Oscillator (SHO) • When the restoring force is directly proportional to the displacement from equilibrium, the resulting motion is called simple harmonic motion (SHM). • An ideal spring obeys Hooke’s law, so the restoring force is F x = –kx, which results in simple harmonic motion.
Key definitions. Simple harmonic motion. Displacement, x – the distance from the equilibrium position. Amplitude, A – the maximum displacement. Period, T – the time taken to complete one full oscillation. Frequency, f – the number of oscillations per unit time.
Coupled Oscillators • Assume solutions are of the form b( ) c( ) = b c cos − • Then, + d − − d − d + d − b c =0 • You must be able to calculate the eigenvalues of a 2x2 or 3x3 matrix. – Calculate the determinant – Calculate the roots by factoring the determinant or using the quadratic formula.
