Spring constant in mass spring combinations

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mrcotton
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Homework Statement



How do we derive the total spring constants of different mass spring systems

Homework Equations



F= kΔx

The Attempt at a Solution



Handwritten derivation of springs in series: two springs k1 and k2 hang in a column with force F_total at the bottom, showing F_T = F1 + F2, F = kΔx, Δx_T = Δx1 + Δx2, and final result 1/k_T = 1/k1 + 1/k2.
 
Handwritten notes on parallel springs: two springs k1 and k2 hang side by side from a bar with a mass below, forces F1 and F2, total force FT = F1 + F2, displacement Δx_T = Δx1 = Δx2 labelled total displacement, F = kΔx, and k_T = k1 + k2.


In the parrallel case I can see how the displacement is the same but again I am confused by the forces.
I guess I need a couple of spring balances