The Differential Equation $\frac { d ^ { 2 } x } { d t ^ { 2 } } + x e ^ { 0.01 x } = 0$

question 16

Multiple Choice

The differential equation $\frac { d ^ { 2 } x } { d t ^ { 2 } } + x e ^ { 0.01 x } = 0$ is a model for an undamped spring-mass system with a nonlinear restoring force. The initial conditions are $x ( 0 ) = 0$ , $x ^ { \prime } ( 0 ) = 1$ . The solution of the linearized system is

• A) \(x = \left( e ^ { t } + e ^ { - t } \right) / 2\)
• B) \(x = \left( e ^ { t } - e ^ { - t } \right) / 2\)
• C) \(x = \cos t\)
• D) \(x = \sin t\)
• E) \(x = \cos t - \sin t\)

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