What is the potential energy of the spring?

[zachmgilbert]

Homework Statement

What is the potential energy of the spring?
mass=.52 kg
velocity=-6.54sin(20.1t)
time=40.84 seconds
amplitude=.33 meters
angular frequency=20.1

Homework Equations

U =1/2kx²

The Attempt at a Solution

I used x=Acos(wt) and got .2 meters for x. I know this is right.I don't know how to find k.

 

[JaWiB]

x=Acos(wt)

This solution only satisfies the differential equation m\ddot{x}=-kx if \omega^2 = k/m

 

[Char. Limit]

What is \omega^2?

 

[zachmgilbert]

angular frequency squared

 

[Char. Limit]

OK.

If I may ask, what is the independent variable in x=Acos(wt)? I'd like to solve it...

 

[Winzer]

OK.

If I may ask, what is the independent variable in x=Acos(wt)? I'd like to solve it...

Hello Char!

The independent variable is time(t) right? The position(x) depends on it.

You now have x,t & k, you should be able to solve for U.

 

[Char. Limit]

Ah, I have the an-word (answer comes from an-swear, meaning "an-word")

I actually wanted to prove the diff e.q. That was mentioned, but I got carried away. The answer is..

Spoiler

Aaaaaaaauuuggh...

Hello Winzer!

 

[ideasrule]

The Attempt at a Solution

I used x=Acos(wt) and got .2 meters for x. I know this is right.I don't know how to find k.

Then how come the amplitude is 0.33 m?

Anyhow, if you're absolutely sure it's 0.2 m and not 0.33 m, w^2=k/m.