Harmonic Equation!

[Ramulala]

Question - A buoy oscillates in simple harmonic motion as waves go past. The buoy moves a total of 16 feet from its high point to its low point, and it returns to its high point every 8 seconds. Write and equation that describes the motion of the buoy, where the high point corresponds to the time t = 0. h(t) =

The question is asking for an equation in this t = 0. h(t) form? I am not sure how would you write it.

Is this works t=16h(8) ?????

 

[Dr.Peterson]

Question - A buoy oscillates in simple harmonic motion as waves go past. The buoy moves a total of 16 feet from its high point to its low point, and it returns to its high point every 8 seconds. Write and equation that describes the motion of the buoy, where the high point corresponds to the time t = 0. h(t) =

The question is asking for an equation in this t = 0. h(t) form? I am not sure how would you write it.

Is this works t=16h(8) ?????

There is no such thing as "t = 0. h(t) form". You are misreading that.

They are telling you, first, that the high point on the graph is at t=0 (so that a cosine will work well), and then they are asking you to write an expression for h(t).

So find the amplitude and period, and write a function in the form h(t) = __ cos(__t).

 

[Ramulala]

So is this right!

h(t)= 16cos(pi/4 t)

Amplitude is 16
and period will pi/4 because 2pi/8 = pi/4.

I have to submit the answer.

 

[skeeter]

amplitude is not 16 ... high to low is 16

 

[Ramulala]

would the amplitude be 16/2 = 8

 

[lex]

Yes

 

[Dr.Peterson]

So is this right!

h(t)= 16cos(pi/4 t)

Amplitude is 16
and period will pi/4 because 2pi/8 = pi/4.

I have to submit the answer.

would the amplitude be 16/2 = 8

Your pi/4 is right, but it isn't called the period!

Now, to convince yourself that you are right, rather than ask someone else, you can plug in a few times to see if you get appropriate results. Try a time when it should be high (other than 0), and a time when it should be low, and see if it works right. Or put it in a grapher to see if the result looks right.