Exercise 34 Page 105

First, let's graph the position of the yo-yo with respect to the $\text{stage}.$ Since we hold our hand $4\text{ ft}$ above the stage and the string is $3\text{ ft}$ long, the maximum and minimum distance of the yo-yo to the stage will be $4\text{ ft}$ and $1\text{ ft},$ respectively.

If we let go of the yo-yo at time $t=0,$ its starting position is $4\text{ ft}$ and it will go down until it reaches its $\text{minimum}$ $\text{distance}$ from the $\text{stage}.$ Then it bounces back to its $\text{maximum}$ $\text{distance}.$ Let's assume it takes $2$ seconds to go down and another $2$ seconds to go back up. This means that the yo-yo completes $1$ round trip in $4$ seconds.

The motion of the yo-yo is called a cyclical motion. It repeats its motion in regular intervals or periods. Its graph will look like a wave when we connect these points. Let's do it!

Since the $\text{stage}$ is $3.5$ ft above the $\text{auditorium}$ $\text{floor},$ we can translate the graph $3.5$ units up to graph the position with respect to the $\text{auditorium}$ $\text{floor}.$

Finally, we can remove the unnecessary parts and have our graph.