Where does the crate permanently come to rest?

[Doppler]

A small crate of weight 5.0N is released from rest at a height 2.0m up a smoyj inclined plane. The crate slides down the plane and across a smooth 1.50m floor to a rough plane where a spring is located.
The bottom of the spring is located at a height of 0.5m. The spring constant is 20N/m .
The coefficient of kinetic friction between the rough plane and crate is $\frac{1}{\sqrt{3}}$ and the coefficient of static friction is $\frac{1}{\sqrt{2}}$/

(a) What is the max height the crate reaaches on the right hand inclined plane?
(b) Where does the crate permanently come to rest? How many times does the crate travel up to the rough plane?

 

[Päällikkö]

https://www.physicsforums.com/showthread.php?t=4825

Hint: Energy-work principle.

 

[Doppler]

The first part is OK for me,
but the second part seems very complicated.

 

[Päällikkö]

Well, how much must the spring compress in order to keep the crate going?