Damped, Maintained, Forced Oscillations, and Resonance

Comprehensive vocabulary flashcards covering the theory of damped, maintained, and forced oscillations, including the phenomenon of resonance and related physics formulas.

Damped Oscillation

An oscillation whose amplitude decreases over time.

Cause of Damping

Energy loss due to work done by friction and environmental resistance forces.

Maintained Oscillation

A damped oscillation provided with extra energy to compensate for friction loss without changing the natural period of the system.

Forced Oscillation

An oscillation occurring under the influence of a periodic external forcing force, where the system oscillates with the frequency of that external force.

Resonance

A phenomenon where the amplitude of forced oscillation reaches a maximum value because the frequency of the external force ($f$) equals the natural frequency ($f_0$) of the system.

Under-damped Oscillation

Occurs when resistance is small; the object continues to oscillate with decreasing amplitude and stops after several cycles.

Critically Damped Oscillation

Occurs when resistance is just enough that the object returns to a temporary equilibrium position in a short time without completing a single cycle.

Over-damped Oscillation

Occurs when resistance is very high; the object returns to equilibrium over a relatively long period without completing a single cycle.

Applications of Damped Oscillation

Used in shock absorbers for cars and automatic door closing devices.

Examples of Maintained Oscillation

The movement of a clock pendulum or a person pushing a swing at just the right moments.

Factors affecting Forced Oscillation Amplitude ($A_{cb}$)

Depends on the amplitude of the external force and the difference between the external frequency ($f$) and the natural frequency ($f_0$).

Harmful Resonance

Mechanical resonance that causes damage to structures like buildings, bridges (e.g., Tacoma Narrows), or vehicle frames.

Beneficial Resonance

Used in the sound boxes of instruments like guitars and violins to increase sound intensity.

Energy Transformation in Damped Oscillation

A portion of the system's mechanical energy is converted into heat energy due to resistance.

Resonance and Resistance

The resonance peak is sharper and the maximum amplitude is larger when the environmental resistance is lower.

Amplitude Decrease per half-cycle ($\triangle A$)

In a horizontal spring-mass system with friction coefficient $\mu$, it is calculated as $\triangle A = \frac{2\mu mg}{k}$.

Amplitude Decrease per cycle

In a horizontal spring-mass system with friction, it is calculated as $\triangle A_{cycle} = \frac{4\mu mg}{k}$.

Number of oscillations until stop ($N$)

Determined by dividing the initial amplitude ($A$) by the amplitude decrease per cycle ($\triangle A_{cycle}$), represented as $N = \frac{A}{\triangle A_{cycle}}$.

Mechanical Energy ($W$)

Calculated as $W = \frac{1}{2}kA^2$, which also represents the maximum kinetic energy at equilibrium or maximum potential energy at the amplitude.