Question

What is the time period of a spring with mass m having no mass connected to it?

Answer 1

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.

Answer 2

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

Answer 3

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?

Answer 4

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.

Answer 5

@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

Answer 6

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.



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)