Question

A buoy oscillates in simple harmonic motion y = A cos(ωt) as waves move past it. The buoy moves a total of 4.5 feet (vertically) from its low point to its high point. It returns to its high point every 2 seconds.

(a) Write an equation describing the motion of the buoy if it is at its high point at t = 0.
y=

(b) Determine the velocity of the buoy as a function of t.
v=

Answer 1

No idea where to start with the equation..

Answer 2

well lets start with determing teh equation

Answer 3

So we know that from the max to the min it travles all of 4.5 feet.
We know that the amplitude wich is represented by the A is 1/2 of the total amt
so what is the amplitude?

Answer 4

2.25 of course but the ω in the cos is throwing me off

Answer 5

Yes ok next lets decide the period which is that funny looking w

Answer 6

we know that the period is 2 seconds

Answer 7

since it reaches its maximum every 2 seconds

Answer 8

omega i believe its called, y= 2.25cos(πt)?

Answer 9

then take the derivative of that and I can find velocity right?

Answer 10

lets use k instead of that funny w cuz its neways i dummy variable
so there is a formula 360/k=period
our period in this case is 2
360/k=2

Answer 11

360/2=k
k=180
so our funny w is equal to 180
did u follow?

Answer 12

did you see my reply? lol

Answer 13

Well do u have the equation???
First u gotta determine the equation and then u can determine the velocity

Answer 14

If u want i can give u the equation if u dont want to understand how i got he equation i dont mind to be honest with you

Answer 15

y=2.25Cos(180t)
Now u can find the derivative

Answer 16

I have the equation.. it was in my reply but yes I do understand. 2.25cos(πt)

Answer 17

we have to do everything in terms of π but thanks.

Answer 18

ohhhhhh even the the omega must???

Answer 19

that is weird ohh interesting sorry for wasting ur time i didnt realize that

Answer 20

no its okay

Answer 21

U r ok with the rest right? hahah ik y u got annoyed at me. it happens to me too. Like i dont know like how much u knew and explained the topic as if u didnt get it at all. Ppl do it to me also.

Answer 22

yea, it happens to me too. Hard to tell how much people know but this is for calc I so I better know this stuff lol. When I did it I dropped the π by accident but its correct now. Thanks.

Answer 23

hahahah i finished calc 3 and cant remember calc 1 lol