### three spring system

Posted:

**Fri Oct 09, 2015 4:28 pm**Starting point:

Three masses (m1, m2, m3) of equal mass (m=1) are positioned on a flat service in a triangle shape with equal distance one (d=1). Mass m1 is fixed and positioned at the origion (0,0). As follows mass m2 is placed on the (x,y) cordinate (1/2 , 1/2sqr3 ), and mass m3 is placed on the (x,y) cordinate (-1/2 , 1/2sqr3). Masses m2 and m3 are not fixed. The three masses are interconnected with three special springs (s1, s2, s3). They can either be stretched or pressed. The three springs have the same spring constant (k=1). Spring s1 is located between m1 and m2, spring s2 is located between m1 and m3, and spring s3 is located between m2 and m3. There is no gravity involved and the system is in equilibrium.

Now let there be the following pulls between the three masses:

between m1 and m3: 10N (ten Newton)

between m1 and m2: 10N (ten Newton)

between m2 and m3: 1N (one Newton)

Given this new situation, what will be the distances bewteen de three masses (and the corresponding (x,y) positions of the masses m2 and m3)?

In other words: how much will the springs (s1,s2,s3) be pressed or stretched?

Three masses (m1, m2, m3) of equal mass (m=1) are positioned on a flat service in a triangle shape with equal distance one (d=1). Mass m1 is fixed and positioned at the origion (0,0). As follows mass m2 is placed on the (x,y) cordinate (1/2 , 1/2sqr3 ), and mass m3 is placed on the (x,y) cordinate (-1/2 , 1/2sqr3). Masses m2 and m3 are not fixed. The three masses are interconnected with three special springs (s1, s2, s3). They can either be stretched or pressed. The three springs have the same spring constant (k=1). Spring s1 is located between m1 and m2, spring s2 is located between m1 and m3, and spring s3 is located between m2 and m3. There is no gravity involved and the system is in equilibrium.

Now let there be the following pulls between the three masses:

between m1 and m3: 10N (ten Newton)

between m1 and m2: 10N (ten Newton)

between m2 and m3: 1N (one Newton)

Given this new situation, what will be the distances bewteen de three masses (and the corresponding (x,y) positions of the masses m2 and m3)?

In other words: how much will the springs (s1,s2,s3) be pressed or stretched?