Final answer:
The period of motion for a swinging rack is independent of the number of dresses because, in a simple pendulum, the period is determined by the length of the pendulum and gravity, not by the mass of the suspended object.
Step-by-step explanation:
The period of motion of a swinging clothing rack does not depend on the number of dresses hanging from it because, much like a simple pendulum, the period is only affected by the length of the pendulum and the acceleration due to gravity. This concept is a result of the restoring force being proportional to the displacement and acting opposite to the direction of motion. When studying pendula or oscillating systems, it's important to recognize that the mass of the object in motion does not influence the time it takes to complete one oscillation, provided air friction and other non-conservative forces are negligible. In the example of pendula with different masses but displaced by the same angle, the motion of the pendula will not differ because the period of oscillation is independent of mass. This illustrates the fundamental principle that in simple harmonic motion, such as that of a simple pendulum, the mass is not a factor determining the frequency of oscillation or the period. However, factors like the length of the pendulum and acceleration due to gravity play a crucial role.