# Simple Harmonic Motion

• Mar 19th 2007, 06:36 PM
tukeywilliams
Simple Harmonic Motion
A block is hung on a spring, and the frequency f of the oscillation of the system is measured. The block, a second identical block, and the spring are carried into space. The 2 blocks are attached to the ends of a spring, and the system is taken out into space on a space walk. The spring is extended, and the system is released to oscillate while floating in space. What is the frequency of oscillation for this system, in terms if f
I know the answer is sqrt(2)f . But how do we get this?

Thanks
• Mar 20th 2007, 04:45 AM
topsquark
Quote:

Originally Posted by tukeywilliams
A block is hung on a spring, and the frequency f of the oscillation of the system is measured. The block, a second identical block, and the spring are carried into space. The 2 blocks are attached to the ends of a spring, and the system is taken out into space on a space walk. The spring is extended, and the system is released to oscillate while floating in space. What is the frequency of oscillation for this system, in terms if f
I know the answer is sqrt(2)f . But how do we get this?

Thanks

The frequency of oscillation of a spring can be found using the formula:
f = sqrt{k/M}
where k is the spring constant and M is the reduced mass attached to the spring. (1/M = 1/m1 + 1/m2 where m1 and m2 are the masses attached to each end of the spring.)

On Earth, fE is measured and we have M = m, the mass of the block: fE = sqrt{k/m}
In space, fS is measured and we have M = m/2: fS = sqrt{2k/m}

fS = sqrt{2}*sqrt{k/m} = sqrt{2}*fE

-Dan