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

question 1

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) \(x = 0.1 e ^ { t }\)

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Water frozen into a solid state, which can appear transparent or a more or less opaque bluish-white color, depending on the presence of impurities.

River Terraces

Step-like landforms alongside rivers, formed by the erosion of sediments and changes in water level.

River Terraces

Step-like landforms found alongside river valleys, created as a river cuts downward into its bed while leaving remnant levels of previous floodplain as terraces.

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