Question

the vertical displacement y of a boat that is rocking up and down a lake, with y measured relative to the bottom of the lake. It has a maximum displacement of 12 meters and a minimum of 8 meters, a period of 3 seconds and an initial displacement of 11 meter when measurements was first started (i.e. t=0)

find the the trigonometric function to describe the rhythmic process.

the answer is y(t)=10+2sin(2pi/3(t+1/4))

I was wondering why the phase shift is +1/4 and not -1/4 . Can anyone explain this to me please?

Answer 1

the initial value of 11 means that

2sin(2pi/3(t+1/4)) = 1
sin(2pi/3(t+1/4)) = 1/2

2pi/3(t+1/4) = pi/6
t + 1/4 = 1/4
t=0

With no displacement, y(0) = 0
since sin(x) is a rising curve at x=0, the graph needs to be shifted left to bring the value of 1 into play.

Try playing around here with the values:

http://www.wolframalpha.com/input/?i=10%2B2sin(2pi%2F3(t%2B1%2F4))