Determining a sinusodial equation

[Meeker]

Homework Statement

A boat is tied up at a dock and bobs up and down. The vertical distance between its high and low point is 1.8 m and the cycle is repeated every 4s.

a) Determine a sine equation to model the vertical position, in metres, of the boat versus the time, in seconds.

b) Use your model to determine when, during each cycle, the boat is 0.5 above its mean position. Round your answers to the nearest hundreth of a second.

Homework Equations

y= a sin (k(x-d))+c

Period Length = 2 pi/k

a = amplitude

k = horizonatl stretch/compression

d= horizontal translation

c= vertical translation

The Attempt at a Solution

Not sure If I am correct so far, but I found the amplitude and k value.

A=0.9 (Divided 1.8 by 2) and K = pi/2 ( I found that doing PL = 2pi/k)

Not sure how to get d or c though.

Would appreciate any help. Thanks

 

[HallsofIvy]

Excellent! As for "d" and "c", they depend on your choice of coordinate system: if you take y= 0 to be the mean position of the boat, the c= 0. If, also, you choose t= 0 to be when the boat is at that mean position, then d= 0.