Why response spectrum is represented in acceleration vs frequency?

Force and Stress Generation: Acceleration directly represents the forces in the structure. From Newton’s second law of motion, the force acting on the structure is directly proportional to its mass and its acceleration. The higher the acceleration of ground motion, the higher the induced force in the structure. Which in turn generates higher stresses in the structure.

Energy Transfer: The rate of energy transfer to the structure is proportional to the acceleration of the ground motion. Earthquake generates seismic waves which carry energy. The energy is transferred to the structures through ground motion. According to the work-energy principle, the work done on a structure is equal to the change in its kinetic energy. The work done on the structure is the product of the Force it exerts on the structure and its displacement. As we know force is proportional to the acceleration of ground motion, the higher the acceleration greater the force and work done on the structure hence the faster the rate of transfer of kinetic energy.