An oscillator of mass $M$ is at rest in its equilibrium position in a potential, $V = \frac { 1 } { 2 } k ( x - X ) ^ { 2 }$. A particle of mass $m$ comes from the right with speed $u$ and collides completely inelastic 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: ( $M = 10 , m = 5 , u = 1 , k = 1$ ) (1) $\frac { 2 } { 3 }$ (2) $\frac { 1 } { \sqrt { 3 } }$ (3) $\sqrt { \frac { 3 } { 5 } }$ (4) $\frac { 1 } { 2 }$
An oscillator of mass $M$ is at rest in its equilibrium position in a potential, $V = \frac { 1 } { 2 } k ( x - X ) ^ { 2 }$. A particle of mass $m$ comes from the right with speed $u$ and collides completely inelastic 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: ( $M = 10 , m = 5 , u = 1 , k = 1$ )\\
(1) $\frac { 2 } { 3 }$\\
(2) $\frac { 1 } { \sqrt { 3 } }$\\
(3) $\sqrt { \frac { 3 } { 5 } }$\\
(4) $\frac { 1 } { 2 }$