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hmm. good question. assume that at centre of mass of the spring, a mass 'm' is attached and then just consider the spring itself massless. all other values such as 'k' shall remain constant.
i think if the system (spring + any other mass attached to it) is massless then the spring will not even come down or move when released because it will not have any energy P.E. = mgh
by my previous expression u can see that the spring wudnt move even when you put just a weight mg in the spring it just gets extended and then stops abruptly(no oscillation about mean position) as action mg by spring=reaction -kx(restoring force)by spring so there wud be an extension and then mg acts down ON the body and restoring force keeps it balanced upwards so u need an external force apart from placing a body for oscillation abt a mean position u can also think of it in kunal's lines if there is no energy involved with the spring at rest how can movement take place?
one second. the whole system is NOT massless. the spring HAS mass according to the system. so you do not necessarily consider the spring energy-less.
@apoorvk reading my answer will again will make u realise that the spring wudnt oscillate even when u have a mass attached to it yes it has got some potential energy iu are considerteing the spring to be at some height ]but it has absolutely zero spring energy(due to compression or extension)which is the one that matters for it to oscillate everything in the universe has energy the only question being does it have energy that we are concerned about
LOL, I deleted my reply accidentally. so here we go once again... @salini , you once again have completely misunderstood what i and the question meant up there. i do NOT mean that ANY mass is attached to the spring. look that the question says that the spring ITSELF has a mass 'm'. so, although in ideal cases we consider a 'weight-less' spring, here we have a spring itself that has a weight, and hence a point in space where all its mass can be assumed to be concentrated, aka the CoM. so consider below a situation where the spring lies relaxed on a smooth horizontal surface in a relaxed position, and its CoM at same point. |dw:1333304389288:dw| now, simply imagine the CoM being diplaced by some distance 'x', and think what the motion will be like. do you think no oscillations will occur? will not the CoM oscillate? (lets not think about the amplitude at the moment)
nowhere in the question we are giving an external force for it to get displaced also the asker is talking here abt a spring having a mass attached vertically so the question implies indirectly to a vertical spring case (asking us whether the mass of spring causes oscillation due to gravity) they havent specified any ext.forces so it wud be best that we stick to the data
ofcourse we assume a force!!! do you think it will oscillate if a spring-block system is at equilibrium and no displacement acts on it? the spring itself provides the restoring force everytime. even if its vertical, it works. i am sorry am unable to explain to you.. The spring itself has MASS
if u provide an external force accepted it will oscillate (it ought to due to its elasticity) if not then in both cases the spring remains at rest.