A mass x gram is suspended from a light spring. It is pulled in downward direction and released so that mass performs S.H.M. of period T. If mass is increased by Y gram, the period becomes 4 T / 3 . The ratio of Y / x is

Step-by-step solution

Oscillation Period Ratio Problem The period T of a mass-spring system is given by T = 2 m k , where m is the mass and k is the spring constant. Let x be the initial mass, so T = 2 x k . After adding mass Y , the new mass is x + Y and the new period becomes 4T 3 , leading to 4T 3 = 2 x + Y k . Dividing the second equation by the first eliminates 2 and k , yielding: 4T 3 T = x + Y x Simplifying both sides gives 4 3 = x + Y x . Squaring both sides removes the square root: ( 4 3 )^2 = x + Y x , so 16 9 = 1 + Y x . Solv