Energy conservation vs momentum conservation in SHM

[nikhilarora]

Homework Statement

a mass M , attached to a horizontal spring executes SHM(simple harmonic motion) 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 . the ratio A1/A2 is ...?

Homework Equations

taking angular frequency = ω

The Attempt at a Solution

first taking two mass and spring as the system, since there is no external force momentum remain conserved , applying (M)(ω1)(A1) = (M+m)(ω2)(A2) , i get correct answer but while applying energy conservation equations, i get an incorrect answer!
will energy not remain conserved in such process?

please help!

 

[ehild]

Hi nikhilarora,

You might have done something wrong. Show your work.

ehild

 

[nikhilarora]

Hi nikhilarora,

You might have done something wrong. Show your work.

ehild

using k=spring constant
applying momentum conservation :

M*(ω1)*A1 = (m+M)*(ω2)*A2
=>M*(k/M)^1/2*A1 = (m+M)*(k/m+M)^1/2*A2

=> A1/A2 = (M+m/M)^1/2

applying energy conservation :

1/2 * M*(ω1)² * A1² = 1/2 * (m+M) * (ω2)² * A2²
=> M*(k/M)*A1² = (m+M)*(k/m+M)*A2²
=> A1²=A2²
=> A1=A2

where have i done wrong ??

 

[ehild]

I see. The energy is not conserved when you put the small mass on the vibrating one. It is like an inelastic collision: the masses move together. So the bigger mass has to accelerate up the smaller one, and that happens with the assistance of friction or some other force which does work.

ehild

 

[nikhilarora]

I see. The energy is not conserved when you put the small mass on the vibrating one. It is like an inelastic collision: the masses move together. So the bigger mass has to accelerate up the smaller one, and that happens with the assistance of friction or some other force which does work.

ehild

thanks a lot !