Damped and Forced Oscillations, Resonance Damped Oscillations Damped oscillations involve the gradual decay of the amplitude of an oscillation over time...
Damped and Forced Oscillations, Resonance
Damped Oscillations
Damped oscillations involve the gradual decay of the amplitude of an oscillation over time. This means that the oscillations gradually decrease in size, even if the initial amplitude is large. Examples of damped oscillations include the vibrations of a guitar string when it is plucked, or the damped vibrations of a mass on a spring.
Forced Oscillations
Forced oscillations are when an external force is applied to an oscillating system, causing the amplitude of the oscillations to increase over time. Examples of forced oscillations include the vibrations of a guitar string when a string is plucked, or the vibrations of a mass on a spring when a weight is placed on it.
Resonance
Resonance occurs when an oscillating system experiences forced oscillations with a frequency that is equal to the natural frequency of the system. This means that the amplitude of the forced oscillations is amplified, while the amplitude of the damped oscillations is reduced. Resonance is often seen in musical instruments, such as guitars and pianos, where the natural frequency of the instrument matches the frequency of the plucked string.
Examples
A guitar string that is plucked is an example of a damped oscillation. As the string vibrates, it gradually decays in amplitude until it stops vibrating.
A mass on a spring is an example of a forced oscillation. When the spring is pulled, the mass vibrates back and forth.
A tuning fork is an example of resonance. When the tuning fork is struck, it vibrates and produces a sound that is an exact match for the frequency of the fork