The controlling force curve for spring controlled governors is a straight line. This means that the controlling force exerted by the governor remains constant throughout its operation.

Explanation:

1. Introduction to Spring Controlled Governors:
- Spring controlled governors are mechanical devices used to regulate the speed of engines or machines.
- They consist of a rotating mass called the flywheel or governor ball and a spring.
- The flywheel rotates at a speed proportional to the engine or machine speed.
- The spring provides the controlling force to regulate the speed.

2. Controlling Force in Spring Controlled Governors:
- The controlling force in a spring controlled governor is provided by the spring.
- This force acts on the flywheel to counteract the centrifugal force generated by the rotation.
- By adjusting the force exerted by the spring, the speed of the engine or machine can be controlled.

3. Controlling Force Curve:
- The controlling force curve represents the relationship between the controlling force and the displacement of the governor ball.
- In the case of spring controlled governors, the controlling force curve is a straight line.
- This means that the controlling force remains constant regardless of the displacement of the governor ball.

4. Reason for a Straight Line Curve:
- The reason for the straight line curve is that the spring used in the governor provides a linear restoring force.
- The restoring force is directly proportional to the displacement of the governor ball.
- Therefore, as the governor ball moves away from its equilibrium position, the force exerted by the spring increases linearly.
- This linear relationship between the force and displacement results in a straight line controlling force curve.

5. Importance of a Straight Line Curve:
- The straight line controlling force curve allows for precise control of the speed of the engine or machine.
- By adjusting the spring force, the speed can be accurately regulated.
- This is important for maintaining the stability and efficiency of the system.

In conclusion, the controlling force curve for spring controlled governors is a straight line. This is because the spring used in the governor provides a linear restoring force, resulting in a linear relationship between the force and displacement of the governor ball. This straight line curve allows for precise control of the speed of the engine or machine.