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A mass \( m \) is suspended from a spring of length \( / \) and force constant \( K \). The frequency of vibration of the mass is \( f_{1} \).
\( \mathrm{P} \) The spring is cut into two equal parts and the same mass is

W suspended from one of the parts. The new frequency of vibration of mass is \( f_{2} \). Which of the following relations between the frequencies is correct
[NCERT 1983; CPMT 1986; MP PMT 1991; DCE 2002]
(a) \( f_{1}=\sqrt{2} f_{2} \)
(b) \( f_{1}=f_{2} \)
(c) \( f_{1}=2 f_{2} \)
(d) \( f_{2}=\sqrt{2} f_{1} \)
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