Damped and Driven Oscillations and Wave Mechanics

Vocabulary flashcards focusing on damped and undamped oscillations, wave classifications, sinusoidal wave parameters, and string wave speed formulas.

Oscillatory Motion

The repeated to and fro movement of a system from its equilibrium position.

Restoring Force

A force acting on a system displaced from its fixed point that tries to bring back the system to its fixed point, giving rise to oscillations or vibrations.

Damping

The decrease in amplitude of an oscillation because of energy being drained from the system to overcome frictional or other resistive forces.

Undamped Oscillations

Oscillatory motion whose amplitude remains the same or constant over time.

Underdamped Condition

The condition in which damping of an oscillator causes it to return to equilibrium with the amplitude gradually decreasing to zero, returning faster but overshooting and crossing the equilibrium position one or more times.

Critically Damped Condition

The condition in which the damping of an oscillator causes it to return as quickly as possible to its equilibrium position without oscillating back and forth about this position.

Overdamped Condition

The condition in which damping of an oscillator causes it to return to equilibrium without oscillating, moving more slowly toward equilibrium than in the critically damped system.

Wave

A disturbance in a medium that carries energy without particles being moved.

Mechanical Waves

Waves which need any type of medium for propagation and are not capable of transmitting energy through a vacuum.

Longitudinal Wave

A wave in which particles of the medium vibrate parallel to the direction of propagation of the wave.

Transverse Wave

A wave in which particles of the medium vibrate perpendicular to the direction of propagation of the wave.

Sine Wave

Any oscillation whose waveform is that of a sine curve, representing periodic oscillations in which the amplitude of displacement at each point is proportional to the sine of the phase angle.

Sinusoidal Wave Equation

The mathematical formula $y(x,t) = A \tan(kx - \frac{\text{wt}}{\text{phase}}) \rightarrow y(x,t) = A \tan(kx - \text{wt} + \tan(\theta))$ representing moving waves, given as $y(x,t) = A \tan(\text{phase})$ or $y(x,t) = A \tan(kx - \text{wt} + \tan(\theta))$ or $y(x,t) = A \tan(kx - \text{wt} + \tan(\theta))$ or explicitly $y(x,t) = A \tan(kx - \text{wt} + \tan(\theta))$ as $y(x,t) = A \tan(kx - \text{wt} + \tan(\theta))$ where $x$ is space coordinate, $t$ is time coordinate, $\tan(\theta)$ or phase shift is $\tan(\theta)$, $k$ is wave number, $A$ is amplitude, and $\text{wt}$ is angular frequency.

Frequency

The number of cycles of vibration in each unit of time, measured in Hertz ($\text{Hz}$) where $1\text{Hz}$ equals $1\text{ cycle per second}$.

Wavelength

The distance sound travels during one period, regardless of frequency.

Wave Number

The number of complete wave cycles of an electromagnetic field that exist in $1\text{ m}$ of linear space, expressed in reciprocal meters ($\text{m}^{-1}$).

Speed of Waves in a Stretched String

The propagation speed defined by the formula $v = \frac{\text{F}}{\text{m}}$ inside a square root: $v = \frac{\text{F}}{\text{m}}$ as $v = \frac{\text{F}}{\text{m}}$ represented as $v = \frac{\text{F}}{\text{m}}$ in equation $v = \frac{\text{F}}{\text{m}}$ or $v = \frac{\text{F}}{\text{m}}$ given by $v = \frac{\text{F}}{\text{m}}$ as $v = \frac{\text{F}}{\text{m}}$ where speed depends on string tension $F$ and mass per unit length $\text{m}$ as $v = \frac{\text{F}}{\text{m}}$

Mass Per Unit Length

The ratio of mass to length for a string, represented by the formula $\text{m} = \frac{m}{L}$.