(a) 1.08 J
The elastic potential energy stored in the block at any position x is given by

where
k is the spring constant
x is the displacement relative to the equilibrium position
Here we have
k = 860 N/m
x = 5.00 cm = 0.05 m is the position of the block
Substituting, we find

(b) 1.16 m/s
The total mechanical energy of the spring-mass system is equal to the potential energy found at point (a), because there the system was at its maximum displacement, where the kinetic energy (because the speed is zero).
At the equilibrium position, the mechanical energy is sum of kinetic and potential energy
E = K + U
However, at equilibrium position x = 0, so U = 0. Therefore, the kinetic energy is equal to the total energy found at point (a)

where
m = 1.60 kg is the mass of the block
v is the speed
Solving for v, we find

(c) 1.00 m/s
When the block is at position x = 2.50 cm, the mechanical energy is sum of kinetic and potential energy:

where
E = 1.08 J is the total mechanical energy
m = 1.60 kg is the mass
v is the speed
k = 860 N/m
x = 2.50 cm = 0.025 m is the displacement
Solving for v, we find

Answer:
The type of light and the material of lenz.
Explanation:
1) As the investigation is based on how the thickness of a lens effect the other variable. Thickness of the lenz is independent variable. So Lidia has to experiment with the different thicknesses in order to find the effect on dependent variable.
2) As the investigation is based to find the point where the beam of light is focused. It's a dependent variable and Lidia has no control over it. So the only thing she can do is to measure and observe how it respond to the changes in independent variable.
3) For conclusion, she has to make sure that the other variables are not effecting the output or results that is the beam point where the light is focused. So she must have to kept constant the type of light and material of lenz otherwise she won't be able to discriminate the effect of thickness of lenz from other causes.