2.6 Forced Vibrations and Resonance

2.6 Forced Vibrations and Resonance

Forced Vibrations:

When an external force drives a system at a frequency other than its natural frequency, the system undergoes forced vibrations. The system responds to the driving force and oscillates at the frequency of the force rather than its natural frequency.

Resonance:

Resonance occurs when the frequency of the external driving force matches the natural frequency of the system, resulting in a large amplitude of oscillation. At resonance, the system absorbs energy most efficiently from the external force.

Example:

A playground swing is pushed at regular intervals matching its natural frequency, causing the swing to reach large amplitudes.

Example Problem:

A tuning fork with a natural frequency of 440 Hz is brought near a string instrument. If the string vibrates at a frequency of 440 Hz, what is the phenomenon observed?

Solution:

The phenomenon observed is resonance. The tuning fork causes the string to vibrate at its natural frequency, leading to a significant increase in the amplitude of the string's vibration.