هام وضروووووووووووووي ساعدوني

[fozia]

السلام عليكم ورحمة الله وبركاته
ارجوا من كل من يستطيع المساعده المشاركه في الحل ....
A bead slide on a smooth rod which is rotating about one end in a vertical plane with
* * * *uniform angular velocity ω. Show that the equation of motion is
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m ( d2r / dt2 ) = mrω2 – mg sinωt
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Q.2. Using Hamiltons’s approach, describe the motion of a particle of mass m constrained
* * * *to move on the surface of a cylinder of radius a and attracted toward the origin by a
* * * *force that is proportional to the distance of the particle from origin.
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Q.3. Show that the transformation Q = log [ ( 1/q) sinP ], P = q cotP *is canonical *and hence
* * * *Find the generating function F.
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Q.4. Suppose the potential in a problem of one dimensional of freedom is linearly
* * * *dependent on time, such that the Hamiltonian has the form H = ( p2/2m ) – m A t x,
* * * *where A is constant. Solve the problem by means of Hamilton’s principal function,
* * * *under the initial conditions t = 0, x = 0 and p = mv0.
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Q.5. A meson has a speed 0.8c relative to the ground. Find how far the meson travels
* * * *relative to the ground, if its speed remains constant and the time of flight, relative to
* * * *the system, in which it is at rest is 2 x 10-8 *sec.
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