# Conservation of Energy or Momentum?

1. Apr 28, 2007

Conservation of Energy or Momentum??

A mass M is attatched to a horizontal spring of force constant k fixed on one side to a rigid suppport.(Please imagine the diagram). The mass oscillates on a frictionless surface with time Period T and amplitude A. When The mass is in equilibrium another mass m is gently placed on it. What will be the new amplitude of oscillation.

My approach,
Conservation of energy
1/2 Mw(1)^2A(1)^2= 1/2 (M+m)W(2)^2A(2)^2 where w is omega.
And then on rearranging the terms i got
[A(1)/A(2)]^2 and
w(1)/w(2) on the left hand side i substituted it with (m+M)/(M) since w is inversely proportional to m.
However if i conserved momentum then i do get the right answer. Question When am i supposd to know when to conserve momentum and when to conserve energy.
Anyone to help since my AIEEE examination is tomorrow.

2. Apr 28, 2007

Note here W(1) A(1) stands for initial amplitude and initial angular velocity.