One end of a light spring of force constant K is fixed to a block of mass M placed on a horizontal frictionless surface, the other end of the spring being fixed to a wall. The spring – block system is executing simple harmonic motion of amplitude A and frequency v. When the block is passing through the equilibrium position, an object of a mass m is gently placed on the block. As a result, the frequency of the system becomes v' and the amplitude becomes A' . The ratio v'/v will be,
(MM+m)1/2
The frequency of the system before the object is placed on the block is given by
v=12π(kM+m)1/2
After the object of mass m is placed on the block, the new frequency of the system becomes
v′=12π[kM+m]1/2
∴v′v=(MM+m)1/2