# Frequency of Oscillation, with mass and k value given

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1. Dec 5, 2014

### LaLaLina

1. The problem statement, all variables and given/known data

A mass m = 2.0 kg is attached to a spring having a force constant k = 990 N/m as in the figure. The mass is displaced from its equilibrium position and released. Its frequency of oscillation (in Hz) is approximately _____ .

2. Relevant equations
$\omega=\sqrt\frac{k}{m}$
$T=\frac{2\pi}{\omega}$ $f=\frac{\omega}{2\pi}$

3. The attempt at a solution

m= 2.0 kg
k= 990 N/m
f = ?
omega = sqrt((990N/m)/(2.0kg)) = 22.25 rad/s
f= (22.25 rad/s)/(2pi) = 3.5 Hz

The answer to the problem, is 4.0 Hz. However, I don't believe I should have rounded up. I believe I have made an error in how to solve the problem.

Have I gone wrong in choosing the formulas to use? or
Should I have taken something else into account based on the mention of the equilibrium statement? and if so, what does that imply?
I recall doing another type of spring problem where it went past its point of equilibrium, but we were using velocity and its angle and solving for v using
dy/dt = -A(omega)sin(omega(t)+phi), however I was reviewing the slides before this problem, and it doesn't seem to address the equilibrium.

I thank you for your assistance very much. I'm studying for my final on Monday and I'm trying to be prepared.

2. Dec 5, 2014

### Staff: Mentor

Hi LaLaLina, Welcome to Physics Forums.

Your solution method and result look fine. It's possible that at some point someone changed a parameter in the problem in order to make it a "new" problem, but didn't update the answer key.

3. Dec 5, 2014

### BruceW

your calculation looks fine to me. 3.5 Hz is correct to 2 significant figures and 4 Hz is correct to 1 significant figure. Although, it is weird that your teacher (or professor or book) wrote 4.0 Hz, since this would usually imply 2 significant figures of precision... maybe it is just an error in the book like gneill says

4. Dec 5, 2014

### LaLaLina

Thank you so much. I got an email back from him, and he said I did wonderful. That it was supposed to be an approximation. So, there in lies the answer I guess. I on the other hand am sitting here worrying my brain out over knowing how to do a problem correctly with this final coming up that is 30% of my grade, so I wanted to make SURE I knew what I was doing.

Thank you both for your feedback.I feel much better now.

5. Dec 5, 2014

### Staff: Mentor

Glad we could help. That's what Physics Forums is all about :)

6. Dec 5, 2014

### LaLaLina

Oh my! I just now noticed the T.A.R.D.I.S.
fellow Whovian in the house!

Thanks again.