S.H.M Homework - Why Consider One Mass Only?

[mysqlpress]

Homework Statement

provided in picture

Homework Equations

provide

The Attempt at a Solution

I know how to show ,but I don't understand why we consider one mass only

[PLAIN][PLAIN]http://b.imagehost.org/0195/questionb.jpg

 

[Doc Al]

That looks like two masses connected by a spring. You describe the motion of each mass (with respect to the center) separately, but they are definitely connected.

 

[mysqlpress]

That looks like two masses connected by a spring. You describe the motion of each mass (with respect to the center) separately, but they are definitely connected.

they strecthed at the same time.
so

ma =-kx
a=-(k/m) x
ma=-kx
a= -(k/m)x

but I don't know how to combine as

a=-(2k/m)x

I think it should be a=-(2k/2m)x = -(k/m)x

 

[Feldoh]

I believe that instead of stretching both, you could hold one down and stretch the other twice as far.

 

[mysqlpress]

I believe that instead of stretching both, you could hold one down and stretch the other twice as far.

That means

ma = -k(2x)?
a=(-2k/m)x ?

I am doubt why ma is used instead of 2ma ?
the whole mass of system is 2m ?

 

[Doc Al]

they strecthed at the same time.
so

ma =-kx
a=-(k/m) x
ma=-kx
a= -(k/m)x

If x is the displacement of each mass, the amount of stretch in the spring is 2x.

 

[mysqlpress]

If x is the displacement of each mass, the amount of stretch in the spring is 2x.

but why should we use

ma=-2kx
but not
2ma=-2kx ?
since there are two bob with mass m..

 

[Doc Al]

but why should we use

ma=-2kx
but not
2ma=-2kx ?
since there are two bob with mass m..

Because we are analyzing the motion of each mass separately:

What's the mass? m
What's the stretch of the spring? 2x
What's the force on each mass? -2kx

 

[mysqlpress]

Because we are analyzing the motion of each mass separately:

What's the mass? m
What's the stretch of the spring? 2x
What's the force on each mass? -2kx

Thanks Doc Al.
you do help me a lot