I have a question.

A buoy sitting in the ocean bobs up and down such that the buoy moves vertically 4.2 ft between the max an min points. The buoy takes 9 seconds to move from the highest to the lowest position. Question: How I can define a function that would give you the number of second that have elapsed since started timing given you know the vertical displacement?

Question

I have a question. 

A buoy sitting in the ocean bobs up and down such that the buoy moves vertically 4.2 ft between the max an min points. The buoy takes 9 seconds to move from the highest to the lowest position. Question: How I can define a function that would give you the number of second that have elapsed since started timing given you know the vertical displacement?

alekos · Answer

We have to assume that the motion is SHM or simple harmonic

The equation for this is x = Asin(2pi/T)t  

where A, the amplitude, is half the entire vertical distance travelled, and T,the period, is twice the time it takes to go from highest to lowest position, and x is the vertical displacement,  t is the time.

a bit of maths is required to make t the subject of the equation.

see how you go