Answer:
[tex]y=6sin(\frac{\pi}{4}t)[/tex]
Step-by-step explanation:
This problem is about an harmonic movement. The definition, that relates the given variables in this kind of movement is:
[tex]y=Asin(\omega t)[/tex]
Where [tex]y[/tex] is the vertical displacement, [tex]t[/tex] is the time and [tex]\omega = \frac{2 \pi}{T}[/tex]
So, we just have find the angular frequency and then replace all given values:
[tex]\omega = \frac{2 \pi}{T}=\frac{2 \pi}{8}=\frac{\pi}{4}[/tex]
In this case, the period [tex]T[/tex] is 8 seconds, because according to the problem, half period is 4 second, from the highest point to the lowest, which is half of the complete period.
Now, replacing values:
[tex]y=6sin(\frac{\pi}{4}t)[/tex]
This expression, where [tex]y[/tex] is the height or vertical displacement, gives the height at any point.
