Oscillations
Basics of Oscillations
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An oscillation refers to a repetitive back-and-forth motion around a central value.
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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.
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Displacement is the position of the object from its equilibrium position and can be positive or negative.
Simple Harmonic Motion
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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).
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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.
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Amplitude of an oscillation is the maximum displacement from the equilibrium position.
Fundamental Properties
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Period (T) of an oscillation is the time for one complete cycle of oscillation.
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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.
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Phase describes a specific stage in a cycle of a periodic wave or oscillation.
Types of Oscillations
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Free oscillation occurs when a system is set into motion and left to oscillate without outside influence.
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Forced oscillation occurs when an external force drives the oscillation of a system.
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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
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For wave motion, like light and sound waves, many of these oscillation properties still apply.
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Wave wavelength is the distance over which a wave’s shape repeats.
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Wave velocity (c) is the speed and direction the wave moves, given by the product of frequency and wavelength, i.e., c = fλ.
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Transverse waves are waves where particles move perpendicular to the motion of the wave. Examples include water waves and electromagnetic waves.
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Longitudinal waves are waves where particles move parallel to the direction of the wave. Examples include sound waves and primary seismic waves.
Superposition Principle
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The superposition principle states that when two or more waves meet, the resultant wave is the vector sum of the individual waves.
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Constructive interference occurs when two or more waves meet and their displacements add together to form a larger wave.
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Destructive interference occurs when two waves cancel each other out, leading to a smaller resultant wave.