A performer seated on a trapeze is swinging back and forth with a period of 9.04 s. If she stands up, raising the center of mass of the trapeze + performer system by 39.1 cm, what will be the new period of the system? Treat the trapeze + performer as a simple pendulum.

The new period of the trapeze when the performer stands up will be shorter than the initial 9.04s due to the effective decrease in the length of the pendulum (trapeze) which increases its frequency.

Explanation:

The period of a simple pendulum, such as a trapeze, is given by T = 2π √(l/g), where l is the length of the pendulum and g is the acceleration due to gravity, assuming small angular displacement. When the performer stands up, the center of mass is raised by 39.1 cm, which effectively shortens the pendulum. This will increase its frequency by effectively speeding up its swing time. However, without further details regarding the initial length of the pendulum, we cannot provide a specific numeric answer for the new period. But based on the equation, we can definitively state that the new period will be shorter than the initial 9.04s because l has decreased.

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