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Engineering question on beams and structures

hello,

i was wondering if anybody could help me with a question about structures/beams?

The problem is about a light beam of length 4L, with three weights (all of weight W) that have been placed at equal distances apart on the beam. The beam is simply supported and has young’s modulus E and second moment of area I. The question asks me to find the central deflection of the beam.

The first part of the question asks me to do this using Macauley’s method, which I have done to obtain the answer, (19W(L)^3)/6EI – I have checked with the answer sheet and this is correct. The next part of the question then asks me to confirm the first part by again finding the central deflection of the beam but by using the method of superposition from a selection of the standard equations of central/end deflections for SS beams and end deflections and rotations of cantilevers.

My problem is that I do not understand how to use this method of superposition? Could someone please explain step by step how you use these equations?
Thank you!!

The equations are:

Light Cantilever of length L with weight W at the end:
end rotation: = (W(L^2))/2EI
end deflection: = (W(L^3))/3EI

Cantilever of length L with UDL W=wl:
end rotation: = (W(L^2))/6EI
end deflection: = (W(L^3))/8EI

Light cantilever of length L with a moment M at the end:
end rotation: ML/EI
end deflection: (M(L^2))/2EI

Light SS beam of length L with a weight W supported at the halfway point:
end rotation: (W(L^2))/16EI
central deflection: (W(L^3))/48EI

SS beam of length L with UDL W=wl
end rotation: (W(L^2))/24EI
central deflection: (5W(L^3))/384EI

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