An oscillator of mass M is at rest in its equilibrium position in a potential V=12k(x−X)2. A particle of mass m comes from right with speed u and collides completely inelastically with M and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after 13 collisions is: (M=10,m=5,u=1,k=1).
Initial momentum of mass 'm' = mu =5
Final momentum of system= (M+m)v=mu = 5
For second collision, mass (m=5, u = 1) coming from right strikes with system of mass 15, both momentum have opposite direction.
∴ net momentum = zero
Similarly for 12th collision momentum is zero.
For 13th collision, total mass = 10 +12 × 5 = 70
Using conservation of momentum
Total mass =10+13×5=75
Finald KE of system =12mv2=12×75×
12k A2=12 75×115×115