Maximum separation between blocks on spring

[henry3369]

Homework Statement

Two blocks, each of mass m, are connected on a frictionless horizontal table by a spring of force constant k and equilibrium length L.

Find the maximum and minimum separation between the two blocks in terms of their maximum speed, v_max, relative to the table. (The two blocks always move in opposite directions as they oscillate back and forth about a fixed position.)

Homework Equations

Conservation of energy

The Attempt at a Solution

K_i + U_i = K_f + U_f
K_i = U_f
(1/2)mv_max² = (1/2)kx²
Solve for x and the (1/2) cancel.
So:
x = sqrt(mv_max/k)
This gives the amount the string has stretched, so the distance between the blocks would be x + L which would result in:
Max separation = sqrt(mv_max/k) + L.
When I type in the solution I get a message that his is incorrect because the maximum separation does not depend on v_max.

 

[BvU]

Re-check the step (1/2)mv_max² = (1/2)kx², So: x = sqrt(mv_max/k)

For example with a dimension check.

And: what exactly is v_max if there are two blocks ? Is the centre of the spring fixed to the table ? Don't you have two half springs that way ?

 

[haruspex]

(1/2)mv_max² = (1/2)kx²

In addition to BvU's comments, there are two blocks to store KE but only one spring to store PE.