Question

Two blocks of masses m1 and m2 are connected by a spring of stiffness k.Another block of mass m1 ,sliding at V0 with out friction,hits the set up elastically as shown in the figure.

Plot elastic energy of the spring as a function of time t after the collision.

Answer 1

Due to one dimensional elastic collision of identical bodies, velocity is transferred totally to m1.

Let x1 and x2 be positions of m1 and m2 at a time t. Then extension in the spring (with natural length = l)

x = x2 – x1 – l ...(1)

The equation of motion of m1 is writen as

From these

Solving these,

From(i) and (ii)