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(B) For a forced oscillator,the amplitude $A$ is given by the formula: $A = \frac{F_0}{\sqrt{m^2(\omega^2 - \omega_d^2)^2 + (b\omega_d)^2}}$,where $F_

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$\frac{F_0}{\omega_d b}$

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(B) For a forced oscillator,the amplitude $A$ is given by the formula: $A = \frac{F_0}{\sqrt{m^2(\omega^2 - \omega_d^2)^2 + (b\omega_d)^2}}$,where $F_0$ is the driving force amplitude,$m$ is the mass,$\omega$ is the natural frequency,$\omega_d$ is the driving frequency,and $b$ is the damping constant.When the driving frequency $\omega_d$ is close to the natural frequency $\omega$,the term $(\omega^2 - \omega_d^2)$ becomes very small,approaching zero.In this condition,the amplitude is dominated by the damping term: $A \approx \frac{F_0}{\sqrt{(b\omega_d)^2}} = \frac{F_0}{b\omega_d}$.Thus,the maximum possible amplitude is $\frac{F_0}{b\omega_d}$.

The value of maximum possible amplitude in the case of forced oscillations when the driving frequency is close to the natural frequency is:

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