110年 - 110 國立中山大學_碩士班招生考試_資工系(乙組)：工程數學#105752

科目：中山◆資工◆工程數學 | 年份：110年 | 選擇題數：0 | 申論題數：9

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所屬科目：中山◆資工◆工程數學

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申論題 (9)

1. The following matrix describes a system of linear equations in five unknowns: v, w, x, y, z What is the general solution to this system?

2.1 Find the characteristic polynomial of A.

2.2 Find the eigenvalues for A.

3. Find the impulse and step responses of a system with transfer function.

4.1 In the integral expression for ax above, the integrand and the limits define the signal x(t). Determine an equation for x(t) that is valid over one period.

4.2 Using the result from part 4.1 , draw a plot of x(t) over the range of -8 ≤ t ≤ 8 seconds.

4.3 Determine the DC value of x(t).

5. Find a particular solution of

6. Find the solution of the given initial value by using Laplace transform and inverse Laplace transform.

y"+ 4y = 3 sin(2t), y(0)=2, y'(0)=-1