True or false question for the linearization of a nonlinear system. 1. The matri

Question

True or false question for the linearization of a nonlinear system.

1. The matrix of the linearized system in the Jacobian matrix.

2. The linearized system approximates the nonlinear system near an equilibrium point.

3. The size of the nonlnear terms near the quilibrium point determine how good the linear approximation will be near the equilibrium point.

4. Linearization always works, if we are willing to stay sufficently close to the equilibirum point.

5. If the Jacobian matrix at an equilibrium point has both positive and negative entries (with no zero entries), the equilibrium poin is called a saddle.

6. For simplicity, one can simply cut off the nonlinear terms with a butter knife.

Ture or false question for the resonnat case of undamped sinusoidal forcing:

1. The natural frequency is equal to the external forcing frequency.

2. All solutions oscillate with the natural frequency.

3. For large t, the amplitude of oscillations grows linearly without bound.

Explanation / Answer

1)T

2)F

3)T

4)F

5)T

6)F

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