Thread: SHM

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

Hi there TurkeyWilliams

Here is a quick dirty way of solving that problem:

As there are no external forces acting on the system the centre of mass of the system is at rest. Also as the blocks are the same the displacement from the centre of mass of the blocks is symmetric so let the distance of the blocks from the centre of mass be x.

Now you can imagine this problem as being identical to having two separate springs tied to a nail at the centre of mass in such a way that the original spring is made up of these two smaller identical springs. But then 1/k = 1/k' + 1/k' => k' = 2k

So the frequency of the SHO in space is f' = 1/(2pi) Sqrt(k'/m) = 1/(2pi) Sqrt(2k/m) = Sqrt(2) f

Hope that helps.