A bulet of mass m and velocity v strikes a mass M connected to a spring (k=spring constant) [the spring is placed horizontaly and other end is fixed.]and get embeded to it . Find the amplitude of oscilation.

first applying conservation of momentam

 mv = (M+m)V_f

 V_f = mv/m+M  

now , kinetic energy of block + mass = KE

   KE = (m+M)V_f² /2

  this system will stop moving when its all KE is converted into PE

 so , KE = PE

      KX² = (M+m)V_f²

       X =[ m²v² /(M+m)K ]^1/2  = max amplitude

Approved

please approve my answers if they are correct