ENADE Física Practice Questions - ENADE Física - Exame Nacional De Desempenho Dos Estudantes Exam

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A damped harmonic oscillator of mass $m$, natural undamped frequency $\omega_0$, and damping parameter $\gamma = b/(2m)$ is driven by external periodic force $F(t) = F_0 \cos(\omega t)$. What is the driving frequency $\omega_r$ that maximizes the steady-state position oscillation amplitude $A(\omega)$, assuming underdamping $\gamma < \omega_0 / \sqrt{2}$?

$$\omega_r = \omega_0$ $$\omega_r = \sqrt{\omega_0^2 - \gamma^2}$ $$\omega_r = \sqrt{\omega_0^2 + 2\gamma^2}$ $$\omega_r = \sqrt{\omega_0^2 - 2\gamma^2}$

Correct Answer:

$$\omega_r = \sqrt{\omega_0^2 - 2\gamma^2}$

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