# Simple Harmonic Motion (easy question)

1. Aug 1, 2009

### MarineBio

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

A 0.26 kg mass attached to a spring undergoes simple harmonic motion with a period of 0.84 s. What is the force constant of the spring?

2. Relevant equations

T = 2*pi*SQRT(m/k)

3. The attempt at a solution

I know this is supposed to be an easy question, but for some reason I can't do it. Here is what I got (which is not right):

T = 2*pi*SQRT(m/k) and to solve for "k":

K = 2*pi*SQRT(m)[whole thing divided by .84 seconds] = 3.814 N/m

Ok, so what am I doing wrong? Thanks!

2. Aug 1, 2009

### cepheid

Staff Emeritus
Your algebra doesn't look right. To solve for k, you want to get it by itself on one side of the equation, which involves:

1. Getting rid of the 2pi (by dividing both sides of the equation by 2pi).
2. Getting rid of the square root (by squaring both sides).
3. Getting k on top (taking the reciprocal of both sides)
4. Getting rid of the m (multiplying both sides by m)

3. Aug 1, 2009

### nickmai123

It might make it more clear if it looked like this:

$$T=2\pi \sqrt{\frac{m}{k}}$$

Now solve for k.

HINT: Squaring both sides gets rid of the square root.

4. Aug 1, 2009

### MarineBio

ok so K = (2*pi*m)/T^2

That gives me 2.315 N/m which is also incorrect. Hmm... I don't know.

5. Aug 1, 2009

### Chrisas

You forgot to square the 2*Pi

6. Aug 1, 2009

### MarineBio

Problem solved. Thank you