Final answer:
The equation for displacement in a beam supported at both ends depends on the context, such as static equilibrium conditions with applied weights or Hooke's law for springs. For beams, factors like the weight and distance from support points to applied forces are used in equilibrium equations, while for elastic materials undergoing deformation, the work done is proportional to the square of displacement.
Step-by-step explanation:
The question pertains to the displacement in a physical system. If we're dealing with a bar supported at both ends, the displacement at any point depends on various external factors such as forces applied to the bar. In scenarios involving static equilibrium and elasticity, the second condition for equilibrium is considered for a system under external forces.
For example, in a situation where weight is applied at specific points on the beam, we use the principle of moments or torque to find the net force and thus the displacement. The equation in static equilibrium conditions for a symmetrical beam with weights applied at distances from the support points may look like this: (distance from support to weight 1)(weight 1) + (distance from support to weight 2)(weight 2) = (distance from support to resultant force)FB.
Moreover, displacement related to Hooke's law is represented as x for a system undergoing elastic deformation. When a force is applied to such a system, the work done is given by the area under the force-distance graph, which is depicted as W = (1/2)kx², where k is the stiffness constant of the material and x is the displacement.