Explain the behaviour of the oscillator when the driving frequency is close to natural frequency in small damped oscillation and define the resonance.

Explain the behaviour of the oscillator when the driving frequency is

1.	Explain the behaviour of the oscillator when the driving frequency is close to natural frequency in small damped oscillation and define the resonance.
Answer» Solution :Amplitude of FORCED OSCILLATION `A= (F_0)/([m^(2)(omega^(2)-omega_(0)^(2))^(2)+(omega_(d)^(2)b^(2))]^(1/2))` If `omega_(d)` is very close to `omega`, then `m(omega^(2)-omega_(d)^(2))` is MUCH less than `omega_(d)b` so it is neglected `A= (F_0)/(omega b)`. Hence, the MAXIMUM amplitude for a given driving frequency is governed by the driving frequency and the damping and is never infinity. Resonance : ..The phenomenon of increase in amplitude when the driving force is close to the natural frequency of the OSCILLATOR is called resonance...