Question Detail
Question
The variation with frequency of the amplitude A of the forced oscillations of a machine is as shown in the graph. Which of the following statement is false?
Correct Answer
Option B is the correct answer.
Detailed Explanation
Let's analyze each statement:A. The resonance frequency is the frequency at which the amplitude of oscillation is maximum. From the graph, the peak amplitude occurs at approximately 12 Hz. So, this statement is TRUE.C. Increased damping spreads out the resonance curve, making the peak less sharp (broader) and reducing the maximum amplitude. So, this statement is TRUE.D. As damping increases, the energy dissipated per cycle increases, leading to a smaller maximum amplitude at resonance. So, this statement is TRUE.B. The graph shows a maximum amplitude of 1.5 cm for the given damping. If there were no damping, the amplitude at resonance would theoretically be infinite, or at least significantly larger than 1.5 cm in a real system (limited only by the driving force). Therefore, stating that the maximum amplitude is 1.5 cm 'for no damping' is FALSE; 1.5 cm is the peak amplitude with damping.
Hint
Consider the effect of damping on the amplitude and sharpness of resonance in forced oscillations.