# Two masses attached to a spring

#### guru1323

I am stuck with a problem. There are two point masses with values m1 and m2 respectively. Both are attached to the two ends of a spring with spring constant 'K'. Initially the spring has a elongation = X0, then it is released to follow its natural motion. We have to find the maximum distance traveled by each of the two blocks. Since there are no external forces on the system, will the centre of mass of the system be at rest?

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#### anigeo

listen carefully.
since the two ends of the spring are connected to masses m1 and m2, hence you can consider the two halves of the string on either side of the centre of the string as two different springs connected to a fixed support (the centre).
each of the springs will have spring constant 2K(this can be obtained from some eqns.)
so you are right to think that the centre of mass of the system will be at rest.
however the is smt. wrong with the part of the question which says that the spring has an initial elongation X0.if it's so then X0 is the maxm. displacements of the block
.

#### Doc Al

Mentor
Since there are no external forces on the system, will the centre of mass of the system be at rest?
Yes, that's the key. Hint: What will be the total displacement when the spring is compressed?

#### guru1323

listen carefully.
since the two ends of the spring are connected to masses m1 and m2, hence you can consider the two halves of the string on either side of the centre of the string as two different springs connected to a fixed support (the centre).
each of the springs will have spring constant 2K(this can be obtained from some eqns.)
so you are right to think that the centre of mass of the system will be at rest.
however the is smt. wrong with the part of the question which says that the spring has an initial elongation X0.if it's so then X0 is the maxm. displacements of the block
.
Yes, that's the key. Hint: What will be the total displacement when the spring is compressed?
Thank you both for ur replies...But i dont really understand the reason behind conclusion that COM will not move..I understand that acceleration of COM will be zero since there are no external forces present...but why cant we have a situation where COM moves with a constant velocity (acceleration = 0) till it comes to a maximum compression
@Anigo...X0 is the initial elongation of the whole spring and we have to calculate maximum displacements of the both blocks individually...I think sum of displacements of both blocks will be 2X0(Please correct me if i am wrong)

#### Doc Al

Mentor
But i dont really understand the reason behind conclusion that COM will not move..I understand that acceleration of COM will be zero since there are no external forces present...but why cant we have a situation where COM moves with a constant velocity (acceleration = 0) till it comes to a maximum compression
Since there are no external forces acting, the acceleration of the COM must be zero. Assuming it was released from rest, the COM cannot move.
I think sum of displacements of both blocks will be 2X0(Please correct me if i am wrong)
Sounds good to me.

#### anigeo

you r right in thinking that the COM might move with uniform velocity.but is there any difference between the state of rest and uniform motion.a uniform velocity does not alter or hamper our thing even we assume the COM to0 be at rest.
try to recall the newtons's first law of motion.it says that there is no difference between the state of rest and uniform motion as the accn. in both the cases is 0.
moreover the maxm. displacement of each of the block will be X0.

#### Doc Al

Mentor
moreover the maxm. displacement of each of the block will be X0.
The displacement of each block depends on the ratio of their masses.

#### anigeo

The displacement of each block depends on the ratio of their masses.
could u please explain me how does it happen?please procure the details.

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