88年 - 88 淡江大學轉學考理論力學#56176

科目：轉學考-理論力學 | 年份：88年 | 選擇題數：0 | 申論題數：4

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所屬科目：轉學考-理論力學

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申論題 (4)

1. A particle of mass m has velocity v = a/x ， where x is its displacement. Fin4 the force F(x) responsible, 25%

2, For a system of particles, prove that its total angular momentum about an origin is the sum of the angular momentum of the center of mass about that origin and the angular momentum of the system about the position of the center of mass . 25%

3, Calculate the inertia tensor of a homogeneous cube of density p ，mass M，and side of length b. Let one comer be at the origin，and let three adjacent edges lie along the coordinate axes, 25%

【已刪除】4. Two identical harmonic oscillators (with masses M and natural frequencies

) are coupled such that by adding to the system a mass m common to both oscillators the equations of motion become

Solve this pair of coupled equations, and obtain the frequencies of the normal modes of the system.