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If mass M oscillates on a spring having mass m and stiffness k, then the natural frequency of the system is

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ISRO VSSC Technical Assistant Mechanical 25 Feb 2018 Official Paper
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Explanation:

Let,

S = Spring stiffness, ms = Mass of spring,m = mass of the system,V = velocity given to mass

Consider an element of length dy and mass dm at distance 'y' from the fixed point. As the variation of velocity is linear along the length of spring the velocity of an element ẏ can be written as,

Now the natural frequency of vibration

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