Spring oscillation problem

Dec 2018
2
0
The questions reads: two masses oscillate on light springs. The second is half the first mass, with twice the spring constant of the first. Which system will have greater frequency, and what is the ratio of the frequency of the second mass to the first.

I have T1=2pi x sq rt of m/k
T2=2pi x sq rt of (m/2)/2k=2pi x sq rt m/4k



I've looked at the answer key and the next step has T2=2pi/2 x sq rt m/k, but i'm not seeing how it got there. I assume it's an algebraic process that I don't understand, can anyone help?
 
Oct 2017
642
330
Glasgow
The first part seems correct to me.

Which system will have greater frequency, and what is the ratio of the frequency of the second mass to the first.

I've looked at the answer key and the next step has T2=2pi/2 x sq rt m/k, but i'm not seeing how it got there. I assume it's an algebraic process that I don't understand, can anyone help?
Frequency is related to the period:

\(\displaystyle T = \frac{1}{f}\)

Therefore, the ratio of the frequencies is

\(\displaystyle \frac{f_2}{f_1} = \frac{T_1}{T_2} = \frac{2 \pi \sqrt{\frac{m}{k}}}{2 \pi \sqrt{\frac{m}{4k}}}\)

Have a go at simplifying this to a nicer form... :)
 
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Dec 2018
2
0
I got it now, the issue was I didn't realize I could split the sq. root to get like terms. Thanks