Sharpness of Resonance

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SHARPNESS OF RESONANCE;
WE HAVE SEEN THAT AT RESONANCE, THE AMPLITUDE OF OSCILLATOR BECOMES VERY LARGE, IF THE AMPLITUDE DECREASES RAPIDLY AT A FREQUENCY, THE RESONANCE WILL BE SHARP.THE AMPLITUDE AS WELL AS ITS SHARPNESS,BOTH DEPEND UPON THE DAMPING.SMALLER DAMPING,GREATER WILL BE AMPLITUDE AND MORE SHARP WILL BE THE RESONANCE.

A HEAVILY DAMPING SYSTEM HAS A FAIRLY FLAT RESONANCE CURVE AS IN SHOWN IN AN AMPLITUDE FREQUENCY GRAPH IN FIG[A]
THE EFFECT OF DAMPING CAN BE OBSERVED BY ATTACHING A PENDULUM HAVING LIGHT MASS SUCH AS A PITH BALL AS ITS BOB AND ANOTHER OF THE SAME LENGTH CARRYING A HEAVY MASS SUCH AS A LEAD BOB OF EQUAL SIZE,TO A RODE.THEY ARE SET INTO VIBRATIONS BY A THIRD PENDULUM OF EQUAL LENGTH ATTACHED TO THE SAME ROD.IT IS OBSERVED THAT AMPLITUDE OF THE LEAD IS MUCH GREATER THEN THAT OF THE PITH BALL.THE DAMPING EFFECT FOR THE PITH-BALL DUE TO AIR RESISTANCE IS MUCH GREATER THAN FOR THE LEAD BOB.



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