The correct answer is: A. smaller damping ratio.
A damping ratio is a measure of how quickly a system will return to equilibrium after being disturbed. A system with a high damping ratio will return to equilibrium quickly, while a system with a low damping ratio will return to equilibrium slowly.
An increase in gain will cause the system to oscillate more strongly. This is because the gain amplifies the output of the system, which in turn amplifies the error signal. The error signal is what drives the system to return to equilibrium, so a larger error signal will cause the system to oscillate more strongly.
A larger oscillation will cause the system to spend more time away from equilibrium. This means that the system will have more time to lose energy, and the damping ratio will decrease.
Therefore, an increase in gain will lead to a smaller damping ratio.
Here is a more detailed explanation of each option:
- Option A: Smaller damping ratio. This is the correct answer, as explained above.
- Option B: Larger damping ratio. This is incorrect, as explained above.
- Option C: Constant damping ratio. This is incorrect, as the damping ratio will decrease with an increase in gain.
- Option D: None of the above. This is incorrect, as option A is the correct answer.