Introduction to Oscillations

Oscillations describe the back-and-forth motion of a body or a physical quantity around an equilibrium position (rest position). Classical examples include swings, pendulum clocks, springs with attached masses, rolling balls on inclined planes, liquids in U-tubes, and guitar strings. Non-mechanical oscillations, such as alternating voltages or electromagnetic fields (light), also fall into this category. eriodic oscillations repeat at equal time intervals, e.g., pendulums or alternating current. Aperiodic oscillations proceed irregularly, as in human speech or the motion of a shock absorber. Mechanical oscillations concern the motion of bodies around a rest position. Non-mechanical oscillations include, for instance, fluctuations in voltage or light intensity. Damped oscillations lose energy due to friction, which causes the amplitude to decrease, e.g., a swing or a pendulum clock without energy input. Undamped oscillations maintain their amplitude, e.g., alternating current or light waves. Free oscillations occur without continuous energy supply (for example a swing set in motion once) and are always damped in reality. Forced oscillations are sustained by continuous energy input, e.g., by a weight in pendulum clocks, an air stream in vocal cords, or a power source in alternating current. Mechanical oscillations arise when a body is displaced from its equilibrium position. A restoring force counteracts the displacement and accelerates the body back toward equilibrium. Due to inertia, the body overshoots the equilibrium position, resulting in a periodic motion. Energy is alternately converted between potential and kinetic energy. If the restoring force is proportional to the displacement, the oscillation can be described by sine or cosine functions—these oscillations are called harmonic (for example a spring-mass system, a pendulum at small amplitudes, a liquid pendulum). If the restoring force is not proportional to the displacement, anharmonic oscillations arise (for example a ball on an inclined plane, a pendulum at large amplitudes). Periodic oscillations are characterized by the period T and the frequency f. The period is the time required for one complete cycle, while the frequency indicates how many oscillations occur per second. Period and frequency are inversely related: f = 1/T. Example: A heartbeat repeating twice per second corresponds to 2 Hz, or 120 beats per minute. 00:00 Examples of Mechanical Oscillations 02:10 Examples of Non-Mechanical Oscillations 03:05 Periodic and Non-Periodic Oscillations 03:40 Mechanical and Non-Mechanical Oscillations 04:12 Damped and Undamped Oscillations 05:25 Free and Forced Oscillations 06:34 Formation of Mechanical Oscillations 08:09 Harmonic and Non-Harmonic Oscillations 10:41 Frequency and Period