If a system of forces is in equilibrium, which of the following statements is true?

When a system of forces is in equilibrium, it means that all the forces acting on the object are balanced, resulting in a state where there is no net force acting on the system. This condition is essential in many fields, including mechanical engineering and physics, as it allows structures and machines to remain stable.

The statement that the total upward forces equal the total downward forces is a fundamental principle of equilibrium. In a static system, for an object to remain at rest or to move at a constant velocity, the sum of the forces acting in one direction must be equal to the sum of the forces acting in the opposite direction. This ensures that there is no unbalanced force that could cause acceleration.

The other statements suggest that the system would experience motion, either by vibrating or rotating in a particular direction, which contradicts the definition of equilibrium. Vibrations imply oscillation about an equilibrium point, while clockwise or counter-clockwise rotation indicates that there is a net torque acting on the system, leading to motion rather than a stable equilibrium. Thus, the correct understanding of equilibrium directly supports the validity of the statement regarding the balance of forces.