In high-school physics class, we have learnt that in a system of springs in parallel, the effecting force constant can be expressed as the sum of force constants of all springs in the system.
Is it required that all of these springs should have the same original spring length?
No. Recall that the restoring force of a spring is governed by Hooke's Law:
F=-kx
(F - force; k - spring constant; x - displacement from equilibrium)
Over the range of displacements where Hooke's law applies, the length of the spring plays no role. The force is dependent upon the spring constant and the displacement of the spring from equilibrium.
In a system of springs acting in parallel, the total force is additive for small displacements. If you arrange the system so that all springs have the same displacement, independent of their length, then the effective force constant will be the sum of all the individual force constants. (To do this you could align the free ends and adjust the fixed end of each spring individually until all springs are in equilibrium.)
And, to add to Anastas' remark, for a short spring the non-linearity starts to be noticible for smaller absolute displacements than for a long spring.
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