Mechanics Elastic springs question

[rbnphlp]

A particle of mass m is attached to one end of an elastic spring of natural length l and modulous lambda ..The particle and spring rest on a rough horizontal surface and the other end of the spring is fixed..Th coefficient of friction is mu .the particle is held at rest with the spring compressed to a length 2/3l and then released.Show that the particle is instamtenously at rest when it has a moved a distance x where,..lambda=Y,mu=P
$x=\frac{2Yl-6Plmg}{3Y}$

Can some one check if my assumptions are right?..

First of all they want me to show the velocity is 0..
I use conservation of energy
$\frac{Yl}{18}=\frac{Yx_1^2}{2l}+\frac{1}{2}mv^2$
where $x_1=\frac{2Yl-6Plmg}{3Y}-\frac{l}{3}$
After that I get into big muddle as they don't equal to 0
thanks.

 

[rbnphlp]

anyone please?

 

[Redbelly98]

Can some one check if my assumptions are right?..

First of all they want me to show the velocity is 0..
I use conservation of energy
$\frac{Yl}{18}=\frac{Yx_1^2}{2l}+\frac{1}{2}mv^2$
where $x_1=\frac{2Yl-6Plmg}{3Y}-\frac{l}{3}$
After that I get into big muddle as they don't equal to 0
thanks.

Energy is not conserved here, because of the friction. However, the energy will decrease by an amount equal to the work done by friction.

 

[rbnphlp]

Energy is not conserved here, because of the friction. However, the energy will decrease by an amount equal to the work done by friction.

I forgot about friction thanks..