physcis question

Question

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 positiona.)

Answer 1

Let dL be the largest positive change of L.

By conservation of energy, 

(1/2)k(dL)² = (1/2)mV_max²

Solve for dL,

dL = sqrt(m/k)V_max

L_min = L - dL = L - sqrt(m/k)V_max

L_max = L + dL = L + sqrt(m/k)V_max

 

 

Answer 2

The situation reminds a pendulum oscillating about its vertical line of equlibrium. The speed is maximum at the time when the string takes its original length. In the event when forces of friction are ignored we can apply the law of conservation of mechanical energy being sure that the left and right side dispalcements from the equlibrium position are the same. What comes to mathematical calculations, Mr. Robert J. has alreday shown, and his calculations are correct.