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The left block in figure collides inelas...

The left block in figure collides inelastically with the right block and sticks to it. Find the amplitude of the resulting simple harmonic motion.

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The collision is for a small interval only, we can apply the principal of conservation of momentum. The common velocity after the collision is `(V)/(2)` . The kinetic energy = `(1)/(2) (2m) ((v)/(2))^(2) = (1)/(4) mv^(2)` . This is also the total energy of vibration as the spring is unstretched at this moment. If the amplitude is A, the total energy can also be written as `(1)/(2) kA^(2)` .
Thus `(1)/(2) kA^(2) = (1)/(4) mv^(2) ,` giving A `= sqrt((m)/(2k)) v` .
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