Oscillations

Basics of Oscillations

  • An oscillation refers to a repetitive back-and-forth motion around a central value.

  • A system in equilibrium is crucial for oscillation. This is a state where all forces are at balance and any displacement sets the system into oscillatory motion.

  • Displacement is the position of the object from its equilibrium position and can be positive or negative.

Simple Harmonic Motion

  • If a system’s acceleration is both directly proportional to displacement and in the opposition direction of displacement, the system’s motion is known as Simple Harmonic Motion (SHM).

  • Restoring force is the force that always acts to pull a system back toward equilibrium. In SHM, the restoring force is directly proportional to displacement.

  • Amplitude of an oscillation is the maximum displacement from the equilibrium position.

Fundamental Properties

  • Period (T) of an oscillation is the time for one complete cycle of oscillation.

  • Frequency (f) refers to the number of cycles of oscillation per unit time. Frequency is the reciprocal of the period, i.e., f = 1/T.

  • Phase describes a specific stage in a cycle of a periodic wave or oscillation.

Types of Oscillations

  • Free oscillation occurs when a system is set into motion and left to oscillate without outside influence.

  • Forced oscillation occurs when an external force drives the oscillation of a system.

  • Damped oscillation refers to oscillation where energy is progressively lost over time, usually due to friction or resistance. This causes amplitude to decrease over time.

Characteristics of Wave Motion

  • For wave motion, like light and sound waves, many of these oscillation properties still apply.

  • Wave wavelength is the distance over which a wave’s shape repeats.

  • Wave velocity (c) is the speed and direction the wave moves, given by the product of frequency and wavelength, i.e., c = fλ.

  • Transverse waves are waves where particles move perpendicular to the motion of the wave. Examples include water waves and electromagnetic waves.

  • Longitudinal waves are waves where particles move parallel to the direction of the wave. Examples include sound waves and primary seismic waves.

Superposition Principle

  • The superposition principle states that when two or more waves meet, the resultant wave is the vector sum of the individual waves.

  • Constructive interference occurs when two or more waves meet and their displacements add together to form a larger wave.

  • Destructive interference occurs when two waves cancel each other out, leading to a smaller resultant wave.