Question

an object that weighs 2 pounds is suspended in a liquid. when the object is depressed 3ft from its equilibrium point, it will oscillate according to the formula x=3 cos (8t), where t is the number of seconds after the object is released. how many seconds are in the period of oscillation?

Answer 1

Hello!
Compare your x=3 cos (8t) to
x=a cos (bt), to identify the value of b.

I think you and I went through this sort of comparison before.

What is the value of b?

Answer 2

8?

Answer 3

Yes, and so (I believe) the period is 2Pi/b, or 2Pi/? = ?

Answer 4

2pi/b is the formula

Answer 5

Right. I'm asking you to substitute 8 for b in that formula, to calculate the period.

Answer 6

is pi/4 the answer?

Answer 7

To my mind it is. Our period is Pi/4, which is equivalent to 45 degrees.

But is that what we wanted? the original question asked for the length of the period in seconds, right?

Answer 8

but how did u no to divide it by8?

Answer 9

Let me ask you where that 8 came from.

Answer 10

from the equation they gave us but how did u no to use tht number and not the 3?

Answer 11

I've copied my first comment from the beginning and reposted it here:

Compare your x=3 cos (8t) to
x=a cos (bt), to identify the value of b.

I think you and I went through this sort of comparison before.

What is the value of b?

b is 8, and the standard formula for the period of the cosine function is 2Pi/b.

Answer 12

oh right but what is this formula? x=a cos (bt)?

Answer 13

That's a basic, general formula for the cosine function. a gives us the amplitude; b is the frequency, and t is the independent variable.

There's a matching formula for the sine: y=a sin (bt)

Answer 14

b, I believe, is called the "frequency."

Answer 15

ohh I rem lol

Answer 16

Are you OK with this problem now?

Answer 17

yep :) but I have more ques

Answer 18

I have time for at least one more. Please, would you post it separately? i'll watch for it.

Answer 19

yes hold on plz