If the gain of the critically damped system is increased it will behave asSelect one:a. overdampedb. underdampedc. oscillatoryd. critically damped

If the gain of the critically damped system is increased, it will behave as follows:

1. Determine the initial behavior: A critically damped system initially exhibits a response that quickly reaches its steady-state without any oscillations.

2. Increase the gain: By increasing the gain, the system's response will change.

3. Analyze the new behavior: If the gain is increased beyond the critical damping threshold, the system will no longer be critically damped.

4. Identify the new damping behavior: The new behavior will depend on the specific gain value.

   a. If the gain is increased to a level where the system's response becomes slower and takes longer to reach its steady-state, it will behave as overdamped. In this case, the system will not exhibit any oscillations and will have a slower response compared to the critically damped state.

   b. If the gain is increased to a level where the system's response becomes faster and exhibits oscillations, it will behave as underdamped. In this case, the system will overshoot its steady-state and exhibit oscillatory behavior.

   c. If the gain is increased to a level where the system's response remains critically damped, it will continue to behave as critically damped. This means that the system will quickly reach its steady-state without any oscillations.

Therefore, if the gain of the critically damped system is increased, it can behave as overdamped, underdamped, or remain critically damped, depending on the specific gain value.

If the gain of the critically damped system is increased, it will behave as follows:

1. Determine the initial behavior: A critically damped system initially exhibits a response that quickly reaches its steady-state without any oscillations.

2. Increase the gain: By increasing the gain, the system's response will change.

3. Analyze the new behavior: If the gain is increased beyond the critical damping threshold, the system will no longer be critically damped.

4. Identify the new damping behavior: The new behavior will depend on the specific gain value.

   a. If the gain is increased to a level where the system's response becomes slower and takes longer to reach its steady-state, it will behave as overdamped. In this case, the system will not exhibit any oscillations and will have a slower response compared to the critically damped state.

   b. If the gain is increased to a level where the system's response becomes faster and exhibits oscillations, it will behave as underdamped. In this case, the system will overshoot its steady-state and exhibit oscillatory behavior.

   c. If the gain is increased to a level where the system's response remains critically damped, it will continue to behave as critically damped. This means that the system will quickly reach its steady-state without any oscillations.

Therefore, if the gain of the critically damped system is increased, it can behave as overdamped, underdamped, or remain critically damped, depending on the specific gain value.