# Simple Harmonic Motion

1. Mar 27, 2006

### endeavor

"A 0.25kg mass on a vertical spring oscillates with a frequency of 1.0 Hz. Suppose a 0.50kg mass were instead suspended from the same spring. What would be the frequency of oscillation in this case?"

This is what I did:
$$\frac{f_{1}}{f_{2}} = \frac {\sqrt{\frac{k}{m_{1}}}}{\sqrt{\frac{k}{m_{2}}}}$$
$$\frac{f_{1}}{f_{2}} = \sqrt{\frac{m_{2}}{m_{1}}}$$
$$f_{2} = \frac{1}{4} f_{1}$$
$$f_{2} = 0.25 Hz$$
however, the answer is 0.71 Hz. What did I do wrong?

2. Mar 27, 2006

### Tom Mattson

Staff Emeritus
You got the ratio $m_2/m_1$ wrong. The ratio is 2, which means that $\sqrt{m_2/m_1}=\sqrt{2}$, but you have 4.

So in short I think you squared the 2 when you should have taken the square root.

3. Mar 27, 2006

### endeavor

You are absolutely correct! I didn't realize I did that. Thanks for the prompt reply!