Calculating the mass of the wheel on a pendulum on a watch

[NathanLeduc1]

Homework Statement

The balance wheel of a watch is a thin ring of radius 0.95 cm and oscillates with a frequency of 3.10 Hz. If a torque of 1.1x10^-5 Nm causes the wheel to rotate 45°, calculate the mass of the balance wheel.

Homework Equations

I=mr²
T=(2π)sqrt(I/mgh)
τ=-Kθ

The Attempt at a Solution

I got an answer but it's wrong...

Here's the work I did:
1.1e-5=-K(pi/2)
K=-7.003e-6
19.5 rad/s = sqrt (7.003e-6/(M(0.0095m)²))
380.25 rad/s² = 7.003e-6 Nm / 9.025e-5m M
M*0.0343 m/s² = 7.003e-6 Nm
m = 2.04e-4 kg

The answer should be 0.41g
(I realized just now that I took the square root of a negative number earlier. I tried to redo the problem but I'm still stuck...) Thanks!

 

[SammyS]

Homework Statement

The balance wheel of a watch is a thin ring of radius 0.95 cm and oscillates with a frequency of 3.10 Hz. If a torque of 1.1x10^-5 Nm causes the wheel to rotate 45°, calculate the mass of the balance wheel.

Homework Equations

I=mr²
T=(2π)sqrt(I/mgh)
τ=-Kθ

The Attempt at a Solution

I got an answer but it's wrong...

Here's the work I did:
1.1e-5=-K(pi/2)
K=-7.003e-6
19.5 rad/s = sqrt (7.003e-6/(M(0.0095m)²))
380.25 rad/s² = 7.003e-6 Nm / 9.025e-5m M
M*0.0343 m/s² = 7.003e-6 Nm
m = 2.04e-4 kg

The answer should be 0.41g
(I realized just now that I took the square root of a negative number earlier. I tried to redo the problem but I'm still stuck...) Thanks!

Is that the complete problem, word for word.

It seems that some information is missing. I could guess at what's missing, but it would be just a guess.

 

[NathanLeduc1]

Yep, that's the question word for word.

 

[TSny]

What is 45^o in radians?

 

[NathanLeduc1]

pi/4

 

[NathanLeduc1]

Oh my goodness... I just realized why you were asking me that. Wow, I am dumb. Man, those stupid mistakes get me every time. Thanks for the help.