課程名稱︰普通物理甲上 課程性質︰必修 課程教師︰高涌泉 開課學院：理學院 開課系所︰物理學系 考試日期（年月日）︰97/11/13 考試時限（分鐘）：120 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.A block of mass m is attached to a spring with spring constant k. The block is pulled from its equilibrium position and then released. (a)What is the angular frequency of the resulting simple harmonic motion?(5%) (b)If in addition to the spring force the block is also subject to a damping force (F=-bv, b is the damping constant), what is the angular frequency of the damped oscillation?(10%) 2.What force is needed to cause a body of mass m to move in a straight → ^ line at a uniform velocity ( V =Vo r ) and normal to the axis of ^ → ^ rotation ( z ), as viewed in a frame in uniform rotation ( w = w z )? See Fig. 1 (20%) 3.In Fig.2, a stick of length L oscillates as a physical pendulum. (a)What is the distance x between the stick's center of mass and its pivot point O that gives the least period ?(10%) (b)What is that least period ?(10%) O ／ z ﹨﹨↘ │ ╱﹨﹨ L/2 │ → ^ ﹨﹨ │ path V =Vo r x ﹨﹨↖ │ ↓ ╱﹨﹨／ │-------˙→ ﹨﹨↘ ∕ ＼ m ﹨﹨ L/2 ∕ ＼ ﹨﹨ ∕ ＼ ﹨﹨↖ ∕ ＼ ﹨﹨╱ x y Fig.1 Fig.2 4.In Fig.3, a particle of mass m is a distance d from one end of a uniform rod with length L and mass M. What is the magnitude of the gravitational → force F on the particle from the rod?(10%) → ^ ^ 5.(a)Is the force of the form F(r)=f(r)θ, where θ is a unit vector perpendicular to the radius vector, conservative? Why?(5%) → ^ (b)Is the force F(x,y)=xy^2 i conservative? Why?(5%) ^ ^ (c)Is the force F(x,y)=ky i - kx j ( k is a constant ) conservative? Why? (5%) 6.A uniform rope of mass m and length L hangs from a ceiling. (a)What is the speed of a transverse wave on the rope when the wave is at a distance y from the lower end?(10%) (b)What is the time a transverse wave take to travel the length of the rope?(10%) m M ˙ ▃▃▃▃▃▃▃▃▃▃▃▃ │←d→│← L →│ Fig.3 PS.可以使用計算機 --

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