The top end of a spring is held fixed. A block is hung on the bottom end as in p

Question

The top end of a spring is held fixed. A block is hung on the bottom end as in part [a] of the figure below, and the frequency f of the oscillation of the system is measured. The block, a second identical block, and the spring are carried up in a space shuttle to Earth orbit. The two blocks are attached to the ends of the spring. The spring is compressed, without making adjacent coils touch (as shown in part [b] of the figure below), and the system is released to oscillate while floating within the shuttle cabin (as shown in part [c] of the figure below). What is the frequency of oscillation for this system in terms of f?

- f/2

- f/sqrt(2)

- f

- sqrt(2)f

- 2f

Explanation / Answer

(a) f1 = 2(pi)sqrt(k/m)

f2= 2(pi)sqrt(k/mu) , where mu =m1*m2/(m1+m2) = m^2/2m =m/2

f2= 2(pi)sqrt(2k/m) = sqrt(2)*f1

so (4th) option sqrt(2)*f

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