Why Do Different Conservation Laws Give Different Results in SHM Problems?

[kushan]

Conservation of energy ?

Homework Statement

I was trying to solve this question
" A mass M , attached to a horizontal spring , executes SHM with Amplitude A1 , when the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with Amplitude A2 , ratio of A1/A2 "
when i apply conservation of Momentum i get
(M/(m+M))^(1/2)
and if i apply conservation of energy
i get (M/(m+M)

Can somebody help me figure out what is going wrong ?
Thank you

 

[ehild]

When you place the small mass on the big one while it is in motion, the small mass has to accelerate up, the bigger mass has to decelerate to the common speed. For that, some force of interaction is needed, and that force does work. Because of the work done by something else than the spring, the sum of the elastic energy and kinetic energy is not conserved.
The situation is similar to inelastic collision. If the small mass were put in front of the big one it would be exactly an inelastic collision. The momentum conserves but the energy does not.

ehild

 

[kushan]

thank you ehild :D

 

[ehild]

You are welcome.