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)