Lesson 8, Topic 5
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# Resonance & Forced Vibrations

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### Forced Vibrations:

A body undergoing SHM loses energy slowly due to friction and air resistance and its amplitude decreases gradually until it becomes zero. When the body experiences such type of motion, it is said to be damped, but when the motion is free or undamped it is said to experience free vibrations.

Free vibration is said to occur when an object vibrates on its own after being displaced and released.

Forced vibration occurs when a body vibrates under the continuous influence of an external force which is periodic in nature e.g.

• The vibration of a tuning fork when subjected to a periodic force of sound wave.
• The vibration of a bridge when soldiers are marching on it.
• Tuning of a radio set

### Resonance:

Resonance is said to occur when the forcing frequency of an external oscillation or vibration matches a body’s natural frequency, and as a result either causes it to vibrate or increases its amplitude of oscillation.

A bodyâ€™s own frequency is better referred to as its natural frequency (f0).

Resonance occurs when the forcing frequency (ff) of a body equates to the natural frequency i.e (ff = f0).

Examples of resonance are seen;

• When you drop a tool or a plate on the ground. The clang produced is caused by the tool or plate vibrating at its resonant frequency.
• When car bodies rattle at certain speeds. This is induced in parts of the car when the natural frequency coincides with the frequency of vibration of the car engine.
• When divers attain a maximum lift by timing their bounce on the diving board with the natural frequency of the diving board.

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