Question

When an external force with angular frequency \( \omega_0 \) acts on a system of natural angular frequency \( \omega \), the system oscillates with angular frequency \( \omega_d \). The condition for the amplitude of oscillations to be maximum is:

• A. \( \omega_d = 2 \omega \)
• B. \( \omega_d = \omega \)
• C. \( \omega_d = \frac{\omega}{2} \)
• D. \( \omega_d = 3 \omega \)

Hint:

For resonance in oscillations, ensure that the angular frequency of the external force matches the natural frequency of the system.

Answer 1

The Correct Option is B

For maximum amplitude in oscillations, the driving frequency must match the natural frequency of the system. Therefore, the condition for maximum amplitude is \( \omega_d = \omega \). Thus, the correct answer is option (2).