The Differential Equation $\frac { d ^ { 2 } x } { d t ^ { 2 } } + x \cos x = 0$

Multiple Choice

The differential equation $\frac { d ^ { 2 } x } { d t ^ { 2 } } + x \cos x = 0$ is a model for an undamped spring-mass system with a nonlinear forcing function. The initial conditions are $x ( 0 ) = 0.1$ , $x ^ { \prime } ( 0 ) = - 0.1$ . The solution of the linearized system is

A) $x = 0.1 \cos t$
B) $x = 0.1 \sin t$
C) $x = 0.1 \cos t - 0.1 \sin t$
D) $x = 0.1 e ^ { - t }$
E) $x = 0.1 e ^ { t }$