# Simple Harmonic motion of vertical spring.

1. Dec 11, 2008

### Kizaru

1. The problem statement, all variables and given/known data
An object of unknown mass M is hung from a vertical spring of unknown spring constant k, and the object is observed to be at rest when the spring has extended by 14cm. The object is then given a slight push and executes SHM. Determine the period of this oscillation.

2. Relevant equations
T = 1/f
w = (k/M)^(1/2) = 2pi*f
F=kx

3. The attempt at a solution
The object is hanging, so it has a force of Mg pulling it down and kx pulling it up. It's in equilibrium at a displacement of 14cm (0.14m). So I set kx = Mg and solved for k:
k = Mg / x

I then plugged this into w = (k/M)^(1/2) so the M's cancel and I'm left with w = (g/x)^(1/2) = (9.8 / 0.14)^(1/2) = 70rad/s

w = 2pi*f => f = w/(2pi) = 11.14 Hz
T = 1/f = 0.089s

This isn't the right answer according to the book, and I keep getting this kind of problem wrong. I'm not entirely sure what I'm doing wrong.

2. Dec 11, 2008

### rl.bhat

3. The attempt at a solution

I then plugged this into w = (k/M)^(1/2) so the M's cancel and I'm left with w = (g/x)^(1/2) = (9.8 / 0.14)^(1/2) = 70rad/s

Check the above calculation

3. Dec 11, 2008

### tiny-tim

Hi Kizaru!

(have a square-root: √ and an omega: ω )
Nooo … √70

4. Dec 11, 2008

### Kizaru

Ah yes, turns out my mistake was ignoring the square root. Thanks. I made that same mistake for all of these types of problems hehe, thanks :) Embarassing, guess I should check for elementary mistakes before I look for physics mistakes :)