Answer

For some values of the constant k the sequence approaches the equilibrium point directly. The graph below illustrates this behavior.

For some values of the constant k the sequence overshoots the equilibrium, then undershoots it, then overshoots it, and so forth, eventually approaching the equilibrium. The graph below illustrates this behavior.

For some values of the constant k the sequence overshoots the equilibrium, then undershoots it, then overshoots it, and so forth, but the swings get wider and wider moving further and further away from the equilibrium. The graph below illustrates this behavior.