Spring, Fs
We are going to suppose that Hooke's Law will govern the force as the spring exerts on the object. This force will all the time be present suitably and is
Fs = -k ( L + u )
The Law of Hooke tells us that the force exerted through a spring will be the spring constant, k > 0, times the displacement of the spring by its natural length. For our set up the displacement from the spring's natural length is as L + u and the minus sign is in there to ensure that the force all the time has the accurate direction.
Let's ensure that this force does what we expect this to. If the object is at rest into its equilibrium position the displacement is L and the force is simply Fs = -kL that will act in the upward position since it must since the spring has been stretched from its natural length.
If the spring has been stretched additionally down from the equilibrium position so L + u will be positive and Fs will be negative acting to pull the item or object back up as it must be.
Subsequently, if the object has been moved up past its equilibrium point, although not yet to its natural length so u will be negative, but even less than L and thus L + u will be positive and once again Fs will be negative acting to pull the object up.
At last, if the object has been moved upwards hence the spring is now compressed, so then u will be negative and greater than L. Hence, L + u will be negative and here Fs will be positive acting to push the object down.
Therefore, it looks like this force will act as we expect that it must.