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A spring of force constant k is initially in vertical position as shown and the massless...

A spring of force constant k is initially in vertical position as shown and the massless metallic plate at its top is at position 0 =y . Then a magnet of mass m falls down onto the plate from rest and from the height H y + = (g is acting down).   



a- Find the lowest value of y at which the magnet and the plate reach just after the inelastic collision (writing the necessary conservation principle).

  

b- Find the value of y at which the magnet and the plate reach the equilibrium position without further vertical oscillations.

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