How Do Masses Move With a String Instead of a Spring?

[aiyiaiyiai]

Homework Statement

Two particles of equal mass (m) on a smooth horizontal table are connected by the a thin elastic string of natural length (a) in which a tension mg would produce an extension (a). The particles are held at rest at a distance (3a) apart.
i. Describe their motions between the time they are released and when they collide.
ii. If the particles are released simultaneously, calculate the time elapsed before they
collide, given a = 0.20 m.

Relevant Equations

F=kx
T=2*pi*sqrt(m/k)

I understand the masses will accelerate toward each other with the same varying speed before they reach the natural length of the spring. Then they continue to approach each other while compress the spring, that'll slow their speeds down definitely. So my question is, how could we calculate how long they take for the slowing-down process?

 

[vela]

What you wrote would be true for a spring, but you don’t have a spring in this problem. You have a string.

 

[Lnewqban]

I understand the masses will accelerate toward each other with the same varying speed before they reach the natural length of the spring elastic string. Then they continue to approach each other while compress the spring, that'll slow their speeds down definitely at constant velocity once the distance between them has reached the value of a (natural length of the elastic string).

For each particle, you have acceleration from repose along distance a, and then constant final velocity along distance 0.5a (point of impact).
Note that the acceleration is caused by a variable or decreasing tension of the string.

 

[aiyiaiyiai]

For each particle, you have acceleration from repose along distance a, and then constant final velocity along distance 0.5a (point of impact).
Note that the acceleration is caused by a variable or decreasing tension of the string.

OMG, I didn't realize it is a string! thx!

 

[aiyiaiyiai]

yes my bad. I didn't realize it is a string.

What you wrote would be true for a spring, but you don’t have a spring in this problem. You have a string.