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Nov2-11, 07:51 PM
P: 11,678
The tension in the rope is going to vary as the mass moves up and down (this should be obvious, as the spring will change length and so must "administer" a force -kΔx accordingly).

Something to consider is the fact that, thanks to the rope and pulley, the other side of the rope (without the spring) is always going to have the same tension as the side with the spring. This assumes a massless pulley without friction or rotational inertia of course.

Since the tension versus displacement is the same for both ropes, the system behaves as though BOTH ropes have a spring in them! So what is the effective spring constant for two springs in parallel?