Question

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

• A. $\frac{F_{0}}{m\left(\omega^{2}-\omega_{d}^{2}\right)}$
• B. $\frac{F_{0}}{\omega_{d} b}$
• C. $\frac{F_{0}}{m \omega^{2}}$
• D. $\frac{-F_{0}}{m \omega_{d}^{2}}$

Answer 1

Answer: (B)

The amplitude of forced oscillation,
$A=\frac{F_{0}}{\left\{m^{2}\left(\omega^{2}-\omega_{d}^{2}\right)^{2}+\omega_{d}^{2} b^{2}\right\}^{1 / 2}}$
when driving frequency $\omega_{d}$ is close to natural frequency $\omega$, so we can take $\left(\omega_{d}=\omega\right)$.
Hence, $A=\frac{F_{0}}{\omega_{d} b}$.