what are some of the mathematical problems to be worked out for a high trapeze act in a circus?

Solution-1:
In circus, trapeze is a short horizontal bar hung with the help of ropes or metal straps from a support. It is an example
of aerial apparatus which are commonly found in circus performances. Trapeze acts may be static, spinning, swinging
or flying, etc.
The trapeze artists swing back and forward across the circus ring performing somersaults and catches. It can be
thought of as a pendulum. Time-period is a time taken to complete one swing. Time-period mainly depend upon the
length of the pendulum. By changing the body position trapezist can change can change length of pendulum so that
the period of their swing.
Equation for time period can be given as:
√



Equation shows that the longer length it will lead to longer period and shorter length shorter period. It only depends
upon length l as the acceleration due to gravity remains constant.
So, mathematical problem which can be worked out are periodic motion, harmonic motion, in which sine or cosine
curve will be obtained.
Solution-2:
Below images are shown to illustrate the problem of trapeze.
As we have already mentioned that by changing their body position, the trapezist can change the length of the
pendulum which changes the period of their swing.
By seeing the diagram below these type of problems can be mathematically modelled as periodic flow and can be
solved for the periodic flow with time...