Question
Write the differential equation for damped forced oscillations and discuss the conditions of resonance.
Solution
The differential equation for damped forced oscillation is,
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Solution of the above differential equation is,
Resonance is the state of vibration in which the oscillator oscillates with maximum amplitude.
Thus, the condition of resonance is that A should be maximum.
Therefore denominator of equation (2) should be minimum.
Substituting
in equation (2), we get
The oscillator is in the state of resonance if the frequency of external force is given by,
Solution of the above differential equation is,
Resonance is the state of vibration in which the oscillator oscillates with maximum amplitude.
Thus, the condition of resonance is that A should be maximum.
Therefore denominator of equation (2) should be minimum.
Substituting
in equation (2), we get The oscillator is in the state of resonance if the frequency of external force is given by,
