A weightless spring which has a force constant fr oscillates with frequency f when a mass m is suspended from it. The spring is cut into two halves and a mass 2 m is suspended from one of the halves. The frequency of oscillation will now be:

A weightless spring which has a force constant fr oscillates with frequency f when a mass m is suspended from it. The spring is cut into two halves and a mass 2 m is suspended from one of the halves. The frequency of oscillation will now be:

A
f
B
2f
C
$f / 2^{\frac{1}{2}}$
D
$f \times 2^{\frac{1}{2}}$

Solution:

Spring constant of each halves = 2 k
$f' = 2 π \sqrt{\frac{2 k}{2 m}} = 2 π \sqrt{\frac{k}{m}} = f$

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