What a I doing wrong? Swing/pendulum Questioj

[dantechiesa]

apologies for the misspellings in the title, typed on my phone.

1. Homework Statement
You are in a swing in which the seat is 3.30 m from the suspension bar. You have managed to get the amplitude of your motion up to 2.05 m. If the period of your swing is 3.65 s, what is your speed when you are the bottom of your swing? Give your answer in km/h.

Homework Equations

mgh = .5mv^2[/B]

The Attempt at a Solution

The length of the swing: 3.3, with an ampltiude of 2.05.
Therefore we can calculate the height the swing achieves,
square root ( 3.3² - 2.05²)
This gives roughly 2.586 (which I left un rounded in the calculator)
3.3 - 2.586 gives the height the swing achieves = ~.7139 (again, left unrounded)

Then I calculated the velocity using mgh = .5mv²

m(9.8)(.7139) = .5mv²
m's cancel

square root (9.8* .7139 / .5) = 3.74 m/s, which I then changed to 13.5 km/hr (which is my final answer unrounded)

This answer is incorrect and i can't figure out why.

 

[Mister T]

If you were on a swing and managed to "get your amplitude up to 2.05 m" what would that mean? That you've reached a height of 2.05 m, or that the distance along the arc is 2.05 m? I honestly don't know, but either way it seems the way you've calculated the height can't be right.

 

[Mister T]

Another thing you might think about is whether or not the swing is a simple harmonic oscillator. Hint, they give you the period!

 

[dantechiesa]

I've got nothing, is there anything you can give me to point me in the right direction?

All we have learned in SHM, no equation relates the velocity and amplitude/period, nor is there anyway to find height.

 

[haruspex]

Another thing you might think about is whether or not the swing is a simple harmonic oscillator. Hint, they give you the period!

With that amplitude, it isn't. The period doesn't really help.

 

[haruspex]

reached a height of 2.05 m,

It could not be that. Amplitude is the magnitude of displacement each way from some central position, so a total range of 4.1m.
Horizontal displacement does seem the most likely interpretation, but it might be worth trying arc length.

 

[Mister T]

With that amplitude, it isn't. The period doesn't really help.

Well, realistically, yes. But if you want to be realistic the given period wouldn't be correct, would it?

 

[Mister T]

I've got nothing, is there anything you can give me to point me in the right direction?

All we have learned in SHM, no equation relates the velocity and amplitude/period, nor is there anyway to find height.

Where in its swing does the pendulum have its maximum speed? And don't you have an equation that relates the amplitude to the maximum speed of a simple harmonic oscillator?

 

[haruspex]

Well, realistically, yes. But if you want to be realistic the given period wouldn't be correct, would it?

That's my point, the period is not helpful. It should be much more reliably calculated from the amplitude via energy. That said, we do not really know the pendulum length - the mass centre will be higher than the seat.
So, yes, it would be worth going the amplitude and period route, at least to see how different the answer is.

All we have learned in SHM, no equation relates the velocity and amplitude/period

So what equations do you have for SHM? You did not quote any in the template.